A woman went to the beneficial Loan Company and borrowed $3000. She must pa $119.67 in the end of each month for the next thirty months.

1. Calculate the nominal annual interest rate she is paying to within ± 0.15%.

2. What effective annual interest rate is she paying

 

Answer:

(Part A)

If monthly interest rate be r, then

$119.67 x P/A(r%, 30) = $3,000

P/A(r%, 30) = 25.0689

From P/A Factor table, P/A(1%, 30) = 25.8077 and P/A(2%, 30) = 22.3965. So r lies between 1% and 2%.

Using interpolation,

(r - 1) / (2 - 1) = (25.0689 - 25.8077) / (22.3965 - 25.8077)

r - 1 = (-0.7388) / (-3.4112)

r - 1 = 0.22

r = 1.22%

(Part B)

Effective annual rate = (1 + Monthly rate)¹² - 1 = (1.0122)¹² - 1 = 1.1566 - 1 = 0.1566 = 15.66%