I’m not sure how to solve this

Question

How long (in years and months) will it take for an investment to double 13% compounded monthly?

Answer 1

Hi Lexi:

This is a common type of compound interest problem.

The compound interest formula: A = P(1 + i%/100)ⁿ

where A = final amount, P = principal invested, i = int rate % per period, n = # of compounding periods

Let the amount invested be P => Amount = 2P since the investment doubles

Let the required time be n years.

∴ 2P = P (1 + 13%/12)¹²ⁿ [interest is compounded monthly @ 13%/12 per month for 12n months

2 = (1 + 0.01083333)¹²ⁿ [dividing both sides by P

2 = 1.01083333¹²ⁿ

Since the unknown is an exponent ( a power), we take logs on both sides

ln 2 = 12n x ln 1.01083333

12n = ln 2 / ln 1.010833333

n = 5.36 years

The 0.36 years are 0.36 x 12 months = 4.3 months

So, it takes 5 years and 5 months to double (rounding up to the nearest month)