Question

1. You have just turned 23 years old. Your aunt gave you $ 1,000 for your birthday. You will use the money to open a bank account. The account has a quarterly return of 12 percent. How much do you expect to have in the account on your 65th birthday? explain process Step by Step?

Answer 1

In the question, it is not clear if the interest rate is 12% per quarter, or 12% per year compounded quarterly. We solve using both possibilities as below :

Interest rate is 12% per quarter

Future value = present value * (1 + r)t

where r = quarterly rate of interest. This is 12%.

t = number of quarters in investment period. Number of quarters from age 23 to 65 = number of years * 4 = 168.

Future value = $1,000 * (1 + 12%)168

Future value = $185,621,299,427

Interest rate is 12% per year compunded quarterly

Future value = present value * (1 + (r/n))n*t

where r = annual rate of interest. This is 12%.

n = number of compounding periods per year. This is 4, as the compounding is quarterly.

t = number of years in investment period.  

Future value = $1,000 * (1 + (12%/4))4*42

Future value = $143,434.54