Question

Assume you put $1,200 into an account today at a bank and leave it there for 5 years. The bank promises that there will be $1,440 in the account at the end of the five years. What is the stated rate of interest (APR) on the account if interest is compounded monthly?

please show your work

Answer 1

Present value = PV = $1200

Time in years = 5 years

Future value after 5 years = FV = 1440

It is given that the interest is compounded monthly.

No. of periods (months) = n = 5*12 = 60

Monthly interest rate = rm

Future value is calculated using the formula:

FV = PV*(1+rm)n

1440 = 1200*(1+rm)60

(1+rm)60 = 1440/1200

(1+rm)60 = 1.2

1+rm = (1.2)1/60

1+rm = 1.00304331411956

rm = 0.00304331411956

APR = rm*12 = 0.00304331411956*12 = 3.65197694346993% ~ 3.65% (Rounded to two decimals)

Answer -> APR = 3.65%