If you want to know the time your sum would take to double in 7 years, then divide 72/7(ROI). It comes to approx 10%. Similarly, if you want to double your sum in 9 years, then the ROI at which your sum should grow to double is 72/9 = 8 years.
This is the Rule of 72 which elaborate it.
The Rule of 72 is a quick and simple technique for estimating one of two things:
- the time it takes for a single amount of money to double with a known interest rate, or
- the rate of interest you need to earn for an amount to double within a known time period.
The rule states that an investment or a cost will double wh
If you want to know the time your sum would take to double in 7 years, then divide 72/7(ROI). It comes to approx 10%. Similarly, if you want to double your sum in 9 years, then the ROI at which your sum should grow to double is 72/9 = 8 years.
This is the Rule of 72 which elaborate it.
The Rule of 72 is a quick and simple technique for estimating one of two things:
- the time it takes for a single amount of money to double with a known interest rate, or
- the rate of interest you need to earn for an amount to double within a known time period.
The rule states that an investment or a cost will double when:
[Investment Rate per year as a percent] x [Number of Years] = 72.
I just went through this process myself and it can be a little tricky if you don’t know what you’re looking for. The movie “The Wolf Of WallStreet” comes to mind when shopping for financial advisors…here’s how to not get “Wolfed”!
There are many kinds and specialties of financial advisors - but overall the BEST kind of financial advisor is called a fiduciary. They are legally obligated to put your investment returns first and can lose their license if they try any other investment shenanigans.
Thanks to the internet, there are sites dedicated to finding vetted fiduciary advisors in your area.
Wha
I just went through this process myself and it can be a little tricky if you don’t know what you’re looking for. The movie “The Wolf Of WallStreet” comes to mind when shopping for financial advisors…here’s how to not get “Wolfed”!
There are many kinds and specialties of financial advisors - but overall the BEST kind of financial advisor is called a fiduciary. They are legally obligated to put your investment returns first and can lose their license if they try any other investment shenanigans.
Thanks to the internet, there are sites dedicated to finding vetted fiduciary advisors in your area.
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Hi, this is an interesting question with a simple answer!
You can calculate this by a simple formula called the rule of 72 !
If you want to double your money in ‘n’ years, just divide ‘n’ into 72 to find the required interest rate. r=72/y ; where r=rate of interest and y=no of years
This this case since we are looking at 7 years: r= 72/7 ; y=7years
72/7= 10.3%
So you will need an annual rate of 10.3% to double your investment in 7 years!
Similarly by working it backwards you can find the number of years required to double your investment at a certain rate of interest then the formula is :
y=72/r ; wh
Hi, this is an interesting question with a simple answer!
You can calculate this by a simple formula called the rule of 72 !
If you want to double your money in ‘n’ years, just divide ‘n’ into 72 to find the required interest rate. r=72/y ; where r=rate of interest and y=no of years
This this case since we are looking at 7 years: r= 72/7 ; y=7years
72/7= 10.3%
So you will need an annual rate of 10.3% to double your investment in 7 years!
Similarly by working it backwards you can find the number of years required to double your investment at a certain rate of interest then the formula is :
y=72/r ; where y=no of years and r=rate of interest
Hope this helps :)
Hello,
Please read about the Rule of 72. 72 is a magic number.
It can help you in 2 ways:
- If you want to know the time your sum would take to double in 7 years, then divide 72/7(ROI). It comes to approx 10%.
- Similarly, if you want to double your sum in 9 years, then the ROI at which your sum should grow to double is 72/9 = 8 years.
This is my first answer on quora. Please upvote if you find it useful.
DKP
The Rule of 72
The Rule of 72 is a simple formula that helps you estimate how long it’ll take for your initial investment to double by compounding interest. The formula states:
72 ÷ Rate of Return = Number of years to double initial investment
So if you’re earning 10.2%, for instance, it would take 24 years to double your investment (72 ÷ 10.2= 7 years ).
The Rule of 72 has its limitations. It gives you an estimate based on a one-time investment but for more advanced calculations that include ongoing payments towards your investment or rate changes you might want to consider using an interest calc
The Rule of 72
The Rule of 72 is a simple formula that helps you estimate how long it’ll take for your initial investment to double by compounding interest. The formula states:
72 ÷ Rate of Return = Number of years to double initial investment
So if you’re earning 10.2%, for instance, it would take 24 years to double your investment (72 ÷ 10.2= 7 years ).
The Rule of 72 has its limitations. It gives you an estimate based on a one-time investment but for more advanced calculations that include ongoing payments towards your investment or rate changes you might want to consider using an interest calculator.
The Bottom-Line
If you’re saving for retirement, make compound interest and time work for you. The sooner you start saving the better.
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Where do I start?
I’m a huge financial nerd, and have spent an embarrassing amount of time talking to people about their money habits.
Here are the biggest mistakes people are making and how to fix them:
Not having a separate high interest savings account
Having a separate account allows you to see the results of all your hard work and keep your money separate so you're less tempted to spend it.
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The rule of 72 will help us to calculate this easily.
R * T = 72
Where R is rate of interest and
T is time
With R as unknown, T = 7. Let's substitute in the above formula.
So R = 72/7 = 10.2857
So the amount will double itself in 7 years with an interest rate of 10.29%
Hope you understand.
Thank you reading!
The compound interest paid annually
R=? P=100. t =7 A =200
A = P (1 + R / 100)^t
200 = 100 ( 1 + R /100)^7
log 200 = log 100 + 7 log (1+R/100)
log (1+R/100) = log 200—log 100 / 7 = (2.3010 — 2.000) / 7
1+ R / 100 = A. L. 0.043
1 + R / 100 = 1.104
R / 100 = 1.104 — 1
R / 100 = 0.104
R = 0.104 x 100
R = 10.4 %
Hence rate of interest is 10.4%
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The Rule of 72 is a shortcut that is used to estimate the number of years required to double your money at a given interest rate.
The formula is
Years to double = 72/Rate of interest
In case of your question,
7.5 =72/Rate of interest
Rate of interest = 9.6%
Your investment would have to earn compound interest of 9.6% to double in 7.5 years.
- A= P(1+x)^7
- here A= 2P So A/P= 2
- So(1+x)^7= A/P= 2
- Taking logirthm on both sides we get 7x log (1+x)= log2
- So log(1+x)= log2÷7
- log(1+x) = 0.3010÷7= 0.043
- So (1+x)= 10^ 0.043 = 1.1041
- Therefore rate of interest= 10.41%
I once met a man who drove a modest Toyota Corolla, wore beat-up sneakers, and looked like he’d lived the same way for decades. But what really caught my attention was when he casually mentioned he was retired at 45 with more money than he could ever spend. I couldn’t help but ask, “How did you do it?”
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Mos
I once met a man who drove a modest Toyota Corolla, wore beat-up sneakers, and looked like he’d lived the same way for decades. But what really caught my attention was when he casually mentioned he was retired at 45 with more money than he could ever spend. I couldn’t help but ask, “How did you do it?”
He smiled and said, “The secret to saving money is knowing where to look for the waste—and car insurance is one of the easiest places to start.”
He then walked me through a few strategies that I’d never thought of before. Here’s what I learned:
1. Make insurance companies fight for your business
Most people just stick with the same insurer year after year, but that’s what the companies are counting on. This guy used tools like Coverage.com to compare rates every time his policy came up for renewal. It only took him a few minutes, and he said he’d saved hundreds each year by letting insurers compete for his business.
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Let P = Rs.x. , A = Rs.2x. , t = 7 years. , r = ?
A = P. ( 1 + r/100)^t .
or , 2x = x. ( 1 + r/100)^7.
or , 2 = ( 1. + r/100)^7.
or , log 2 = 7.log (1. + r/100).
or, 0.3010 = 7. log (1. + r/100).
or , log (1+ r/100) = 0.3010/7.
or , log (1 + r/100) = 0.0430.
or, (1 + r/100) = Antilog 0.0430.
or , (1 + r/100) = 1.1041.
or , r/100 = 0.1041. => r = 10.41 %. Answer.
- A=P(1+x)ⁿ
- here A= 2P
- n= 7.5- years.
- So n= log(2)÷ log (1+x) (or)
- log (1+x) = log(2)÷ n
- log(1+x)= 0.3010÷7.5= 0.04014
- So (1+x)= 10^(0.04014)= 1.09693
- x=0.09683 Rate of interest which doubles in 7.5- years = 9.683% .
Use the CAGR formula,
CAGR = (2^ (1/T))x 100 )) - 100,where T is period in years.
Here T is 6.5.
CAGR = (2^(1÷6.5) x 100 ) - 100= 11.2531476096
Just do this:
The annual interest rate is:
2^ (12/90) x100=
109.68249797, interest rate is 9.682% Annual.
90 is taken as number of months, in place of 7.5 years.
Exact rate of interest is 10.41% as shown below using Excel functions of Time Value of Money.
PV = Present Value = - 100 Rs, negative cashflow, money going from our pocket
FV = Future Value = 200 Rs, positive cashflow, money coming to us
nper = No. of Periods = 7 years
PMT = Pament per period (Installment)
RATE : 10.41%
= RATE(nper, PMT, PV, FV) =RATE(7, 0, -100, 100) =10.41%
There is a simple trick employing what is known as Rule of 72.
If interest is 6%, then money doubles in 12 years.
If interest is 8%, then money doubles in 9 years.
If interest is 9%, then money doubles in 8 years.
If interest is 12%, then money doubles in 6 years.
And so on.
So the answer would be 72/7 ie 10 years and a little over 3 months.
Let x be amount invested.
Let r be the rate of interest.
Period = 7.5 years
Hence, x( 1 + r/100)^7.5 = 2x
( 1 + r/100)^7.5 = 2
Solving we get, r = 9.68%
Answer: 10.3%
Step-by-step explanation:
simple trick , use 72/n if compound interest is doubled
here n is 7
so 72/7 = 10.3%
Let i be the rate of interest.
(1+i)^7=2 as the sum doubles in 7 years
1+i =2^(1/7)=1.104089514
i =0.104089514
Or 10.41% p.a. approximately
You can use the formula A=P(1+r)^n by assuming value for P and twice of that as A where n will be 7 and solve the equation to get value of r .
2x=x(1+r)^7 or 1+r=(2)^1/7=1.1041 so r+.1041 or 10.41% per annum is compound interest rate at which investment will be double in 7 year.
for making money doubles in 7 Years you need to gain interest 10.40
% every year with a compound effect.
Simply use Rule of 72 that states 72/ Interest Rate equals Number of years it takes for Investment to double. By that logic, 2 = 72/7 which gives you 10.285%.
Let P be 1.
1 x (1 + r/100) ^ 5 = 3..
1 + r/100 = 3 ^(1÷5)
1 + r/100 = 1.2457309396
r/100 = 0.2457309396
r =.24.57309396
Interest rate is 24.57%
General format, to get value in a flash,
r = (3^ (1÷5) ×100 ) -100
r = (x ...
Let P be 1.
1 x (1 + r/100) ^ 5 = 3..
1 + r/100 = 3 ^(1÷5)
1 + r/100 = 1.2457309396
r/100 = 0.2457309396
r =.24.57309396
Interest rate is 24.57%
General format, to get value in a flash,
r = (3^ (1÷5) ×100 ) -100
r = (x ...
Use the rule of 72.
In order to double in seven years 72/7,you’d have to earn close to 10% compounded every year
Imagine you have ₹10,000 and someone tells you that in just 2 years, it will become ₹20,000, without you adding a single rupee. Sounds exciting, right? But the big question is at what interest rate does this magic happen?
Whenever you put your money in a bank, it grows based on interest. If the bank pays compound interest, your money grows not only on the initial amount but also on the interest you earned in previous years.
The formula to calculate compound interest is:
where:
- A = Final amount (₹20,000 in our case)
- P = Principal (Initial amount, ₹10,000)
- r = Interest rate per year (This is what we n
Imagine you have ₹10,000 and someone tells you that in just 2 years, it will become ₹20,000, without you adding a single rupee. Sounds exciting, right? But the big question is at what interest rate does this magic happen?
Whenever you put your money in a bank, it grows based on interest. If the bank pays compound interest, your money grows not only on the initial amount but also on the interest you earned in previous years.
The formula to calculate compound interest is:
where:
- A = Final amount (₹20,000 in our case)
- P = Principal (Initial amount, ₹10,000)
- r = Interest rate per year (This is what we need to find)
- t = Time in years (2 years)
Since the money doubles, we can write:
Cancel P from both sides:
Taking the square root on both sides:
Since √2 is approximately 1.414, we get:
Subtracting 1 from both sides:
Multiplying by 100:
What Does This Mean for You?
For your money to double in 2 years, you need an interest rate of 41.4% per year, compounded annually.
Now, let’s be real such a high interest rate is extremely rare in safe investments like fixed deposits, savings accounts, or bonds. Banks typically offer 6-8% per year, which means your money would take around 9-12 years to double, not 2 years!
Where Can You Find Such High Returns?
If someone promises to double your money in 2 years, they are likely offering a high-risk investment such as:
✅ Stock Market (Equities) – May be Possible but involves High risk on Principle.
✅ Cryptocurrency – Some coins have done it, but also crashed
✅ Startups & Venture Capital – High risk, high reward
✅ Ponzi Schemes – BEWARE! Many scams promise "double money" but vanish overnight 🚨
A Simple Rule to Remember – The Rule of 72
A quick way to estimate how long your money takes to double is:
If the rate is 41.4%, then:
This rule helps you make quick, smart investment decisions!
Thoughts 💡
If someone promises to double your money in 2 years, ask yourself: is the interest rate realistic? If it's too good to be true, it probably is. Always research, diversify, and invest wisely!
Would you take the risk for 41.4% annual returns, or would you prefer a safer investment? Let me know your thoughts! 🚀💰
Compound Interest Formula: A=P(1+r/n)^nt; where A=$7,166.25, P=$6,500, n=1 for being compounded annually, t=2, r=?, nt=1(2)=2
7,166.25=6,500(1+r/1)^1(2)
7,166.25/6,500=(1+r)^2
1.1025=1+2r+r^2
1.1025–1=2r+r^2
0.1025=2r+r^2
r^2 + 2r - 0.1025=0 Quadratic Equation
Using Quadratic Equation Formula:
r={-2+-[(2)^2–4(1)(-0.1025)]^1/2}/2(1)
r={-2+-[4+0.41]^1/2}/2
r={-2+-[4.41]^1/2}/2
r={-2+-[2.1]}/2
There are 2 values for r:
r={-2+2.1}/2=0.1/2=0.05
r={-2–2.1}/2.=-4.1/2=-2.05 (negative not valid)
Adopt r=0.05 or 5% (answer for interest rate)
Check using the formula for compound interest:
A=6,500(1+.05/1)^2=6,500(1.05)^2
Compound Interest Formula: A=P(1+r/n)^nt; where A=$7,166.25, P=$6,500, n=1 for being compounded annually, t=2, r=?, nt=1(2)=2
7,166.25=6,500(1+r/1)^1(2)
7,166.25/6,500=(1+r)^2
1.1025=1+2r+r^2
1.1025–1=2r+r^2
0.1025=2r+r^2
r^2 + 2r - 0.1025=0 Quadratic Equation
Using Quadratic Equation Formula:
r={-2+-[(2)^2–4(1)(-0.1025)]^1/2}/2(1)
r={-2+-[4+0.41]^1/2}/2
r={-2+-[4.41]^1/2}/2
r={-2+-[2.1]}/2
There are 2 values for r:
r={-2+2.1}/2=0.1/2=0.05
r={-2–2.1}/2.=-4.1/2=-2.05 (negative not valid)
Adopt r=0.05 or 5% (answer for interest rate)
Check using the formula for compound interest:
A=6,500(1+.05/1)^2=6,500(1.05)^2=$6,500(1.1025)
A=$7,166.25 OK
Therefore the answer for interest rate is 5% and confirmed to be correct
It’s actually easy to solve for compound interest.
When interest is added to a deposit balance on an annual basis, for each year the amount grows by the specified percent. To calculate the growth, you add the decimal interest rate to 1 — that is, for 2% interest you add .02 to 1 to get 1.02 — and multiply it times your starting balance once for each year on deposit.
So, for two years, the calculation is Starting Balance x 1.rate x 1.rate = Ending Balance
Notice that 1.rate x 1.rate is 1.rate squared. (The exponent is always the number of years for annual interest payments.)
So, to solve for an unk
It’s actually easy to solve for compound interest.
When interest is added to a deposit balance on an annual basis, for each year the amount grows by the specified percent. To calculate the growth, you add the decimal interest rate to 1 — that is, for 2% interest you add .02 to 1 to get 1.02 — and multiply it times your starting balance once for each year on deposit.
So, for two years, the calculation is Starting Balance x 1.rate x 1.rate = Ending Balance
Notice that 1.rate x 1.rate is 1.rate squared. (The exponent is always the number of years for annual interest payments.)
So, to solve for an unknown interest rate, you want to find that 1.rate squared multiplier, and then find the square root of it to give you the one-year interest rate.
If you divide the Ending Balance by the Starting Balance, the result is the 1.rate squared multiplier.
In this case that’s $7,166.25/$6,500, which gives you a multiplier of 1.1025. If you then use the square root button on the calculator in your phone, you will get 1.05 — which is the multiplier for each year, 1.rate.
So the interest rate is .05 (5 hundredths out of 1), which if you multiply by 100 gives you 5 out of 100, or 5%.
If the term was three years, you would find the cube root. For ten years, the 10th root. For 4 years 3 months, the 4.25th root.
If the interest is paid monthly, you divide the annual interest rate by 12 to find the monthly rate, and then calculate 1.monthlyrate raised to the 12th power to give you the effective annual rate. Use this as the 1.rate multiplier to calculate the interest for every year on deposit.
Use the formul
(((412.6/400)^4)—1) x 100
412.6/400 gives quarterly compounding factor
(412.6/400)^4 gives annual compounding factor.
-1 gives value for 1.
X100 giv
Thus 13.21% is the Annual rate equivalent to 12.6compounded quarterly.
Use the formul
(((412.6/400)^4)—1) x 100
412.6/400 gives quarterly compounding factor
(412.6/400)^4 gives annual compounding factor.
-1 gives value for 1.
X100 giv
Thus 13.21% is the Annual rate equivalent to 12.6compounded quarterly.
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Let us assume that the the two equal amounts are $500.00each.
Based on the above,the total accrued investment for the first $500@ 7%=500(1.07)^4 =$655.40
Similarly,the accrued investment for the second $500.00@5% ————=500(1.05)^4 =$607.75
The total of the two investments for four years at seven ,and five pcent respectively — =$1,263.15
The interest element of the two investments is $(1,263.15 -1,000 ) =$263.15
In order for the interest to double in 20 years,that is $263.15*2 =$526.3
‘Rule 72 in Finance’ which indicates how long it takes an investment to double based a particular interest rate, becom
Let us assume that the the two equal amounts are $500.00each.
Based on the above,the total accrued investment for the first $500@ 7%=500(1.07)^4 =$655.40
Similarly,the accrued investment for the second $500.00@5% ————=500(1.05)^4 =$607.75
The total of the two investments for four years at seven ,and five pcent respectively — =$1,263.15
The interest element of the two investments is $(1,263.15 -1,000 ) =$263.15
In order for the interest to double in 20 years,that is $263.15*2 =$526.3
‘Rule 72 in Finance’ which indicates how long it takes an investment to double based a particular interest rate, becomes a useful tool here.; Simply divide 72 by the interest rate to derive the number of years. In other words at what interest rate will $1,000.00 generate combined interest of $526.3 in 40 years =72/IR=40. IR=72/40=1.8%
Formula, CI=P(1+r/n)^nt -P, where CI=2,448, P=?, r=4%, n=1 considering it is compounding annually, t=4
a. Solving for the principal amount, P, first:
2,448=P(1+0.04/1)^4-P
2,448=P(1.04)^4-P=1.16986P-P=0.16986P
P=2,448/0.16986
P=14,411.90 ( principal amount)
b. Solving for the number of years to earn a compound interest of 2,500 at a rate of 5%;
2,500=14,411.90(1.05)^t-14,411.90
14,411.90(1.05)^t=14,411.90+2,500=16,911.90
(1.05)^t=16,911.90/14,411.90
(1.05)^t=1.1735
Using logarithm:
t log 1.05=log 1.1735
t(0.021189)=0.069483
t=0.069483/0.021189=3.279years
t=3.279 years or 3 years 3 months 11 days
Check:
CI=14,4
Formula, CI=P(1+r/n)^nt -P, where CI=2,448, P=?, r=4%, n=1 considering it is compounding annually, t=4
a. Solving for the principal amount, P, first:
2,448=P(1+0.04/1)^4-P
2,448=P(1.04)^4-P=1.16986P-P=0.16986P
P=2,448/0.16986
P=14,411.90 ( principal amount)
b. Solving for the number of years to earn a compound interest of 2,500 at a rate of 5%;
2,500=14,411.90(1.05)^t-14,411.90
14,411.90(1.05)^t=14,411.90+2,500=16,911.90
(1.05)^t=16,911.90/14,411.90
(1.05)^t=1.1735
Using logarithm:
t log 1.05=log 1.1735
t(0.021189)=0.069483
t=0.069483/0.021189=3.279years
t=3.279 years or 3 years 3 months 11 days
Check:
CI=14,411.90(1.05)^3.279-14,411.90
CI=14,411.90(1.1734)-14,411.90
CI=16,912–14,411.9=2,500 Ok
CAGR =( (EV/SV)^(I/T)) - 1) X 100,
EV IS END VALUE, SV IS start value, T is period in years,
Here EV / SV is 2,
CAGR =( 2^ (1/10)) - 1) X 100.
To arrive daily compounding:
((36500+ R)/36500 )^ 365 = 1.071773462536
(36500 + R)/36500 = 1.071773462536^ (1/365) =
36500 + R = 1.0001899214 X 36500 = 36506.9321311
R = 6.9321311
The daily compounding rate for...
CAGR =( (EV/SV)^(I/T)) - 1) X 100,
EV IS END VALUE, SV IS start value, T is period in years,
Here EV / SV is 2,
CAGR =( 2^ (1/10)) - 1) X 100.
To arrive daily compounding:
((36500+ R)/36500 )^ 365 = 1.071773462536
(36500 + R)/36500 = 1.071773462536^ (1/365) =
36500 + R = 1.0001899214 X 36500 = 36506.9321311
R = 6.9321311
The daily compounding rate for...
The answer is 9%.
Below is the rough but accurate way to calculate the simple interest from Investopedia.
The 'Rule of 72' is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself.
For example, the rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).
When dealing with
The answer is 9%.
Below is the rough but accurate way to calculate the simple interest from Investopedia.
The 'Rule of 72' is a simplified way to determine how long an investment will take to double, given a fixed annual rate of interest. By dividing 72 by the annual rate of return, investors can get a rough estimate of how many years it will take for the initial investment to duplicate itself.
For example, the rule of 72 states that $1 invested at 10% would take 7.2 years ((72/10) = 7.2) to turn into $2. In reality, a 10% investment will take 7.3 years to double ((1.10^7.3 = 2).
When dealing with low rates of return, the Rule of 72 is fairly accurate.
Read more: What is the 'Rule of 72'? | Investopedia
Take a digital spreadsheet like Microsoft Excel and lay it out with one row consisting of 10 cells for the years, and one at the end for a total.
Compute the value of each cell using a standard compound interest formula found in your spreadsheet’s list of formulae and fill in the first 7 cells starting with $4,000,000 in the first one. Each subsequent one is the value of the previous one plus the computed interest. Then subtract $2,305,000 from the 7th cell to fill the 8th cell, and do that again for the 9th and 10th cells.
If you are using a decent spreadsheet, it will have a formula built in t
Take a digital spreadsheet like Microsoft Excel and lay it out with one row consisting of 10 cells for the years, and one at the end for a total.
Compute the value of each cell using a standard compound interest formula found in your spreadsheet’s list of formulae and fill in the first 7 cells starting with $4,000,000 in the first one. Each subsequent one is the value of the previous one plus the computed interest. Then subtract $2,305,000 from the 7th cell to fill the 8th cell, and do that again for the 9th and 10th cells.
If you are using a decent spreadsheet, it will have a formula built in to calculate a discounted cash flow ROI. Apply that formula to your 10–year series of values, and it will very quickly give you your answer.
To find the equivalent periodic rate of 12% compounded annually when compounded monthly, we can use the formula for the effective annual rate (EAR):
EAR = (1 + Periodic Rate)^m - 1
where m is the number of times the interest is compounded per year.
To find the periodic rate, we can use the formula:
Periodic Rate = (1 + Annual Rate)^(1/m) - 1
In this case, the annual rate is 12%, and the interest is compounded monthly, so m = 12.
Substituting these values into the formula, we get:
Periodic Rate = (1 + 0.12)^(1/12) - 1 = 0.01 or 1%
Now we can use this periodic rate and the EAR formula to calculate the e
To find the equivalent periodic rate of 12% compounded annually when compounded monthly, we can use the formula for the effective annual rate (EAR):
EAR = (1 + Periodic Rate)^m - 1
where m is the number of times the interest is compounded per year.
To find the periodic rate, we can use the formula:
Periodic Rate = (1 + Annual Rate)^(1/m) - 1
In this case, the annual rate is 12%, and the interest is compounded monthly, so m = 12.
Substituting these values into the formula, we get:
Periodic Rate = (1 + 0.12)^(1/12) - 1 = 0.01 or 1%
Now we can use this periodic rate and the EAR formula to calculate the equivalent periodic rate when compounded monthly:
EAR = (1 + 0.01)^12 - 1 = 12.68%
Therefore, the equivalent periodic rate of 12% compounded annually when compounded monthly is 1% or 12.68% EAR.
2^0.1=1.07177 for an annual rate of 7.177%
The difference between my answer and others’, which assert 10%, is that the terms are ambiguous.
If you loan $100 and expect $200 to be paid back by the end of 10 years, you’ll receive $10/y (for 9 years) until the 10th year, when you’ll get $110, while if you get all $200 at the end of 10 years, you would not have any annual interest in the intervening time. Yet again, if you got $20/y, there’d be nothing owed after the 10th year, you’d have received $200 as agreed, but your annual rate would be 20% of your initial loan.
If you deposit $100 in a bank an
2^0.1=1.07177 for an annual rate of 7.177%
The difference between my answer and others’, which assert 10%, is that the terms are ambiguous.
If you loan $100 and expect $200 to be paid back by the end of 10 years, you’ll receive $10/y (for 9 years) until the 10th year, when you’ll get $110, while if you get all $200 at the end of 10 years, you would not have any annual interest in the intervening time. Yet again, if you got $20/y, there’d be nothing owed after the 10th year, you’d have received $200 as agreed, but your annual rate would be 20% of your initial loan.
If you deposit $100 in a bank and take out the total at the end of 10 years, and find your withdrawal of $200 empties the account, you will have been getting 7.177% annually. Even so-called simple interest is compounded when the interest is left in the account.
Do you mean that the ratio of amount in 5 years to the amount in 2 years is 119016 ? Such a big ratio may be a typing mistake. I think it will be 1.19016.
Let the Principle = P and rate = r%
So, Amount in 5 years = P * ( 1 + r/100)^5 and Amount in 2 years = P * ( 1 + r/100)^2
By the given condition, the ratio is 1.19016
So, P * ( 1+ r/100)^5 / P * ( 1+ r/100)^2 = 1.19016
Or, ( 1 + r/100)^3 = 1.19016, cancelling P and ( 1 +R)^2 from numerator and denominator
Or, 1 + r/100 = (1.19016)^(1/3) = 1.0597455993
Or, r = ( 1.0597455993 - 1 ) * 100 = 5.97455993% = 5.97% approx. Ans.
I think you mean technically the “annualized interest rate compounded monthly”. Usually effective annual rate is the term for the amount you must get solving for the accumulated value, but here they gave you 2-year effective growth rate . So then the compounded monthly info would be extraneous , but I’ll assume you mean “annualized rate compounded monthly.”
$1,500/$1,200 = 1.25 so the effective 2-year interest rate is given to you it’s 25%.
The effective annual rate is 1.25^(1/2)-1 since (1+i}^T= 1.25 and T=2. = time in years . = 11.8%.
but the annualized rate of interest j when compounding month
I think you mean technically the “annualized interest rate compounded monthly”. Usually effective annual rate is the term for the amount you must get solving for the accumulated value, but here they gave you 2-year effective growth rate . So then the compounded monthly info would be extraneous , but I’ll assume you mean “annualized rate compounded monthly.”
$1,500/$1,200 = 1.25 so the effective 2-year interest rate is given to you it’s 25%.
The effective annual rate is 1.25^(1/2)-1 since (1+i}^T= 1.25 and T=2. = time in years . = 11.8%.
but the annualized rate of interest j when compounding monthly would be such that
(1 + j/12)^12 = 1.118
=[1.118^(1/12) -1]* 12 = 11.209%
ALL of the previous three answers are incorrect, because they have answered the wrong question.
If interest is quoted at a per annum rate, but applied more frequently than once a year (ie, monthly) then the annual rate is called the nominal rate (meaning, “in name only”), and the actual yield achieved by incrementing 1/12th of the interest rate 12 times is the effective rate.
* That is, if the nomi
ALL of the previous three answers are incorrect, because they have answered the wrong question.
If interest is quoted at a per annum rate, but applied more frequently than once a year (ie, monthly) then the annual rate is called the nominal rate (meaning, “in name only”), and the actual yield achieved by incrementing 1/12th of the interest rate 12 times is the effective rate.
* That is, if the nominal rate of 12% p.a. compounded monthly is 1% per month applied 12 times — 1.01 to the 12th power — for an effective annual rate of 12.683%
* If interest is applied annually, there is no difference between the nominal and effective rates
So, if $1,200 grows to $1,500 over two years and you want the effective annual rate of interest, it doesn’t matter whether the interest is compounded monthly, weekly, daily or perpetually:...
Let’s assume you have invested Rs 100 in an investment scheme.
Year 1 : You have a return of 10% and your total amount becomes Rs 110.
Year 2 : You again have a return of 10% but 10% of what? Is it 10 percent of 100 or 110?
Case 1 : If it is 10% of 110, your total amount becomes Rs 121.
Case 2 : If it is 10% of 100, your total amount becomes 120.
Case 1 is an example of compound interest and Case 2 is an example of simple interest.
When your new value becomes the principal/base value for the next calculation, this is know as compounding. The rate at which the value is increasing or decreasing, is kn
Let’s assume you have invested Rs 100 in an investment scheme.
Year 1 : You have a return of 10% and your total amount becomes Rs 110.
Year 2 : You again have a return of 10% but 10% of what? Is it 10 percent of 100 or 110?
Case 1 : If it is 10% of 110, your total amount becomes Rs 121.
Case 2 : If it is 10% of 100, your total amount becomes 120.
Case 1 is an example of compound interest and Case 2 is an example of simple interest.
When your new value becomes the principal/base value for the next calculation, this is know as compounding. The rate at which the value is increasing or decreasing, is known as Compounded Annual Growth Rate or CAGR.
Hope this helps.
Upvote if you think I explained this clearly!
The formula is as follows:
= Amount x (1 + rate) ^ period
The rate and period would need to be adjusted for the period of compounding. In each case the amount is as follows:
Annual compounding
= 10,000 x (1 + 0.04) ^ 2
= Rs. 10,816
Semi annual compounding
= 10,000 x (1 + (0.04/2))^ (2 x 2)
= Rs. 10,824
Quarterly compounding
= 10,000 x (1 + (0.04/4))^ (2 x 4)
= Rs. 10,829
These calculations can be proven from the below calculations:
The formula is as follows:
= Amount x (1 + rate) ^ period
The rate and period would need to be adjusted for the period of compounding. In each case the amount is as follows:
Annual compounding
= 10,000 x (1 + 0.04) ^ 2
= Rs. 10,816
Semi annual compounding
= 10,000 x (1 + (0.04/2))^ (2 x 2)
= Rs. 10,824
Quarterly compounding
= 10,000 x (1 + (0.04/4))^ (2 x 4)
= Rs. 10,829
These calculations can be proven from the below calculations:
What annual interest rate, compounded half yearly, is required if K550 is to grow to K2385 after 6 years?
To calculate the annual interest rate required for an investment to grow from K550 to K2385 after 6 years, compounded semiannually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = Final amount (K2385) P = Principal amount (K550) r = Annual interest rate (to be determined) n = Number of times interest is compounded per year (2, since it's compounded semiannually) t = Number of years (6)
Plugging in the values we know:
2385 = 550(1 + r/2)^(2*6)
Now, let's solve for r:
(
What annual interest rate, compounded half yearly, is required if K550 is to grow to K2385 after 6 years?
To calculate the annual interest rate required for an investment to grow from K550 to K2385 after 6 years, compounded semiannually, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where: A = Final amount (K2385) P = Principal amount (K550) r = Annual interest rate (to be determined) n = Number of times interest is compounded per year (2, since it's compounded semiannually) t = Number of years (6)
Plugging in the values we know:
2385 = 550(1 + r/2)^(2*6)
Now, let's solve for r:
(1 + r/2)^(12) = 2385/550
Taking the twelfth root on both sides:
1 + r/2 = (2385/550)^(1/12)
Subtracting 1 from both sides:
r/2 = (2385/550)^(1/12) - 1
Multiply both sides by 2:
r = 2 * [(2385/550)^(1/12) - 1]
Calculating the right side of the equation:
r ≈ 2 * [1.1814 - 1] r ≈ 2 * 0.1814 r ≈ 0.3628
Therefore, an annual interest rate of approximately 0.3628, compounded semiannually, is required for K550 to grow to K2385 after 6 years.
Using formula
[math]A = {P {(1 + {{r}\over{100}})}^n}[/math]
Given -
in [math]n = 8 [/math] years.
A = 2P
then
[math]2P = {P{(1 + {{r}\over{100}})}^8}[/math]
[math]2 = {{(1 + {{r}\over{100}})}^8}[/math]
[math]{{(1 + {{r}\over{100}})}^8} = 2^{1\over8} [/math]
[math]{{r}\over{100}}= (2^{1\over8} - 1)[/math]
[math]r= 100(2^{1\over8} - 1)[/math]
[math]r= 9.05 [/math] %
please upvote my answer
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