Finite Math- Compounding Quarterly

Question

Eric deposited $5000

 into an account with a 2.4%

 annual interest rate, compounded quarterly. Assuming that no withdrawals are made, how long will it take for the investment to grow to $6000

? Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

If n is the number of quarters, then 5000 ( 1 + (2.4/400))^n = 6000

1.2 = (1 + (2.4/400))^n

ln 1.2 = n ln (1 + (2.4/400))

n = ln (1.2) / ln (1 + (2.4/400))

The 2.4 is divided by 400 ( 4 x 100) because 2.4 is annual %, and there are 4 quarters in a year