Jimmy invests ​$13,000 in an account that pays 7.11​% compounded quarterly. How long​ (in years and​ months) will it take for his investment to reach ​$20,000?​?

Answer 1

Jorie, this question just requires use of the compound interest formula:

A = P( 1 + i/m)^mn

where A = final amount, P = principal invested, i = interest rate per year, n = # of years, m = number of compounding periods per year

Here, 20,000 = 13,000 (1 + 7.11% / 4)⁴ⁿ

=> 20/13 = 1.017775⁴ⁿ

Since n is an exponent, we must use logs on both sides

log (20/13) = 4n log1.017775

=> n = log (10/13) / (4 log1.017775)

I leave the arithmetic for you as an exercise!

This will give n as a whole number of years and a decimal. Multiply the decimal by 12 to convert it to months.