Question

A borrower is faced with choosing between two loans. Loan A is available for $75,000 at 6 percent interest for 30 years, with 6 points to be included in closing costs. Loan B would be made for the same amount, but for 7 percent interest for 30 years, with 2 points to be included in the closing costs. Both loans will be fully amortizing.
a. If the loan is repaid after 20 years, which loan would be the better choice?

b. If the loan is repaid after 5 years, which loan would be the better choice?

Answer 1

Answer:

a) loan A is a better choice

b) loan B is a better choice

Explanation:

the monthly payment of loan A = $449.66

present value of loan A = ($75,000 x 6%) + $75,000 = $79,500

the monthly payment of loan B = $498.98

present value of loan B = ($75,000 x 2%) + $75,000 = $76,500

the difference between monthly payments = $498.98 - $449.66 = $49.32

if we calculate the present value of 20 years paying $49.32 more it is:

PV = $49.32 x 139.58077 (PV annuity factor, 0.5%, 240 periods) = $6,884 which is higher than the difference

if we calculate the present value of 5 years paying $49.32 more it is:

PV = $49.32 x 51.72556 (PV annuity factor, 0.5%, 60 periods) = $2,551 which is lower than the difference