Question

15. To save for retirement, Karla Harby put $625 each month into an ordinary annuity for 14 years. Interest was compounded monthly. At the end of the 14 years, the annuity was worth $156 comma 700. What annual interest rate did she receive? The interest rate she received was approximately _______%. (Round to two decimal places as needed.)

Answer 1

40.08%

Explanation:

From the given information;

the annual interest rate can be determined using the formula:

`A =P *( 1+ (r)/(n))^(nt)`

where;

A = amount

P is the installment per period = $625

r = interest rate

nt = number of installments= 14×(12) =168

i = rate of interest per year

`156700 = 625 *( 1+ (r)/(12))^(168)`

`(156700)/(625) = {(1+ (r)/(12))^(168)`

`250.72 = {(1+ (r)/(12))^(168)`

`\sqrt[168]{250.72} = {(1+ (r)/(12))`

1.0334 =
`{(1+ (r)/(12))`

1.0334 -1 = r/12

0.0334 = r/12

r = 0.0334 × 12

r = 0.4008

r = 40.08%

Thus; Karla Harby received an interest rate of 40.08%