If $5000 is deposited at the end of each quarter in an account that earns 6% compounded quarterly, after how many quarters will the account contain $60,000?

If $5000 is deposited at the end of each quarter in an account that earns 6% compounded quarterly, after how many quarters will the account contain $60,000? (Round your answer UP to the nearest quarter.)

 

FV=P{[1 + R]^N - 1/ R}=FV OF $1 PER PERIOD.

60,000 = 5000{[1 + 0.06/4]^N -1}/ (0.06/4)

Solve for N over the real numbers:
60000 = 333333. (1.015^N - 1)

333333. (1.015^N - 1) = 1000000/3 ((203/200)^N - 1):
60000 = 1000000/3 ((203/200)^N - 1)

60000 = 1000000/3 ((203/200)^N - 1) is equivalent to 1000000/3 ((203/200)^N - 1) = 60000:
1000000/3 ((203/200)^N - 1) = 60000

Multiply both sides by 3/1000000:
(203/200)^N - 1 = 9/50

Add 1 to both sides:
(203/200)^N = 59/50

Take the logarithm base 203/200 of both sides:
Answer: |N = (log(59/50))/(log(203/200))=~11 quarters.