Finding Time Periods

Question

Suppose you deposit $12,000 in a bank account bearing 8.8% interest compounded monthly.

How many months would it take (to the nearest month) for your account balance to top $15,000? Use the trial and error method with a calculator to find your answer.

Answer 1

15000 = 12000 * (1.088) ^ x

 

15000 / 12000 = 1.088 ^ x

 

1.25 = 1.088 ^ x

 

log 1.25 = x * log 1.088

 

x = log 1.25 / log 1.088

 

x = 0.09691 / 0.03663 = 2.646

 

3 months.

 

Where is this bank?  8.8% compounded monthly would work out to 175% per year.

 

Answer 2

12000 x .088 = 1056     12000 + 1056 = 13056 (first month)

 

13056 x .088 = 1148.928      13056 + 1148.928 = 14204.928 (second month)

 

14204 x .088 = 1250.033664      14204 + 1250.033664 = $15404.961664 (third month)

 

Third month would be your answer.