How to solve for i in compounding interest formula A=P(1+i)^n?

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In summary, the formula for compounding interest is (A/P)^1/n - 1 = i. In an example where A is 2, P is 1, and n is 5, the answer should be (2/1)^1/5 - 1 = i. However, some may get the answer of 0.149 by using brackets, while others may get -0.6 by not using brackets. The correct answer is 2^(1/5)-1.
  • #1
cjp88
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I'm having some trouble understanding how to solve for i. This is the formula for compounding interest. I'm reading this example which shows how to solve for i if you double your money in 5 years. So it gives this example:

(A/P)^1/n - 1 = i

So it gives A for 2 and P for 1, n would be 5 so the answer should be:

(2/1)^1/n - 1 = i

They shown the answer as 0.149 however I cannot get this same answer for whatever reason.

When I put in 2/1 I get 2, then 2^1/5 would be 0.4, minus 1 would make it -0.6.

If this answer is indeed right, could someone please show me what I'm missing.
 
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  • #2
[tex]2^\frac{1}{5}[/tex] can't be 0.4, since (0.4)^5 is way smaller than 1 (since 0.4<1).

Since 0.4 = 2/5, you must've raised 2 to the 1th (which is two) and divided that answer by 5.
If you're using a calculator, be sure to put in the brackets correctly: 2^(1/5)-1.
 
  • #3
I see what the problem was, I wasn't using brackets on my calculator. If I do 2^1/5 I get the wrong answer because it does 2^1 which is 2 then divides by 5 to get 0.4 instead of 2^(1/5) being 1.14869...

Thanks for the help on seeing my error.
 
  • #4
Yes, if you just put in "2^1/5", your calculator interprets that as (2^1)/5 = 2/5= .4.
Use 2^(1/5) instead.
 

1. What does A, P, i, and n represent in the equation?

A represents the final amount, P represents the initial principal amount, i represents the interest rate, and n represents the number of compounding periods.

2. How do you solve for i in the equation?

To solve for i, you will need to use logarithms. First, divide both sides of the equation by P. Then, take the natural log of both sides. Finally, isolate i by dividing both sides by n and simplifying.

3. What if the equation has multiple solutions for i?

If the equation has multiple solutions for i, it means that there are multiple interest rates that could result in the same final amount. In this case, you can use trial and error or a graphing calculator to find the exact value of i.

4. Can this equation be used for any type of interest rate?

This equation can be used for any type of interest rate as long as the compounding period is consistent. If the compounding period is not consistent, the equation will need to be adjusted accordingly.

5. How can this equation be applied in real life situations?

This equation can be applied in real life situations to calculate the interest rate needed to reach a certain final amount, or to calculate the amount of time needed to reach a savings goal with a given interest rate. It can also be used to compare different investment options with varying interest rates and compounding periods.

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