Question

A loan of $12,000 is to be repaid within one year with level monthly payments, due at the beginning of each month. The 12 payments equal $1,000 each. A finance charge of $632 is also due with the first payment. Which of the following is closest to the effective annual interest rate on the loan?

(A) 12.7% (B) 12.9% (C) 13.1% (D) 13.3% (E) 13.5%

I'd appreciate it if you could let me know...

Answer 1

At the Interest rate -

Outflow = Inflow

Present Value of Payments = Loan Amount

1000+632 + [1000 x ( PVAF(r%,11))] = 12000

1000 x PVAF(r%,11) = 12000-1632

PVAF(r%,11) = 10368/1000

PVAF(r%,11) = 10.368

Using Annuity Table -

PVAF(1%,11) = 10.9676

This is approximately equal to 10.368

Therefore r = 1% per month Compounded Monthly

Annual interest rate = [(1+0.01)^12]-1

r =[1.01^12 ] -1

r = 12.68%

or

12.70%

Answer is (a)