If 5000 is deposited at the end of each quarter in an accoun

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.)

Solution

The amount after every quarter is given by:

A = 5000[1 + (0.06/4)]^t

for A = 60,000:

60,000 = 5000[1 + 0.015]^t

12 = [1.015]^t

taking log on both sides, we get:

log(12) = t log(1.015)

=> t = 166.89 or 167.

So , after 167 quarters, the amount will be $ 60,000.