# Math Help - How long will it take $10K to grow to... 1. ## How long will it take$10K to grow to...

Hello:

This is a basic finace question (or algebra?); I can't figure out how to solve this manually.

How long will it take for $10,000 to grow to$20,000 at an interest rate of 15% per year?

So:

20,000 = 10,000(1.15)^n
n=4.96 years

I can enter this in to my BA II Plus without issue (and this is fine for my class, but I just want to know what steps to take to work this out manually. I think I missed a whole section of basic math in my studies.

Any help is truly appreciated.

2. Originally Posted by matius
Hello:

This is a basic finace question (or algebra?); I can't figure out how to solve this manually.

How long will it take for $10,000 to grow to$20,000 at an interest rate of 15% per year?

So:

20,000 = 10,000(1.15)^n
n=4.96 years

I can enter this in to my BA II Plus without issue (and this is fine for my class, but I just want to know what steps to take to work this out manually. I think I missed a whole section of basic math in my studies.

Any help is truly appreciated.
Well, we just have to take the simple interest formula, which says what amount P do you have when you have a rate i, an initial amount A, and a time in years n:

P = A(1 + ni)

Which is close, but not exactly what you got. I could not find a single equation that had (1 + i)^n.

So we plug the values above into the equation above:

$20,000 =$10,000 (1 + .15n)

$20,000 =$10,000 + $1500n$10,000 = $1500n 6.667 years = n So that's how long it will take$10,000 to grow to $20,000. 3. Thanks very much for your help, but that makes me a bit confused. n=4.96 is the answer provided by the professor. ...but, still you're saying that you know of no way to manually calculate this answer? That it can only be done via a calculator? Also, wouldn't$10,000(1 + .15) be $11,500 ? Probably basic math, sorry for the confusion!! 4. Originally Posted by matius Thanks very much for your help, but that makes me a bit confused. n=4.96 is the answer provided by the professor. ...but, still you're saying that you know of no way to manually calculate this answer? That it can only be done via a calculator? Also, wouldn't$10,000(1 + .15) be $11,500 ? Probably basic math, sorry for the confusion!!$10,000(1 + .15n) not $10,000(1 + 15) You can't add unlike terms... And if 4.96 is indeed the answer, then just plug everything into the formula: P = A(1 + i)^n$20,000 = $10,000(1.15)^n 2 = 1.15^n This is an exponential equation, so we can reverse the exponent by taking the log base 1.15 of 2, which says what power do you put on 1.15 to get 2. log_1.15 (2) = n Then we use the change of base formula to make it able to be calculated with log base 10, and it looks like this: log(2)/log(1.15) = n Just put it in the calculator and the answer turns out to be: 4.96 = n There you go. Your answer is valid if this equation is used. 5. Perfecto! Thank you... 6. Hello, matius! How long will it take for$10,000 to grow to \$20,000 at an interest rate of 15% per year?

So: .20,000 .= .10,000(1.15)^n