Question

on a $10,000 loan which is paid off by 48 installments of $254 with the first payment due 1 month after receipt of the loan, the annualized rate of interest is _____% on an APR basis. Expressed at an effective compound annual rate, it is ___%

a.8.40;8.73

b.9.24;9.64

c.10.08;10.56

d.11.52;12.15

need calculation steps.

Answer 1

Loan = $ 10000 to be repaid in 48 equal installments of $ 254 each. The compounding is done monthly.

Let the monthly interest rate be R.

Therefore, 10000 = 254 x (1/R) x [1-{1/(1+R)^(48)}]

Solving this equation using EXCEL's Goal Seek Function we get

R = 0.008398 or 0.8398%

Therefore, APR = 12 x R = 12 x 0.8398 = 10.07788% or 10.08% approximately

Effective Compound Annual Rate = [{1+(R/100)}^(12)] - 1 = 0.105567 or 10.56% per annum

Hence, correct answer is option (C) .