Question

Brian mortgaged $200,000 on his house 10 years ago. The mortgage was 25-year fixed rate at 8%. He realizes today that a refinance opportunity is available at 5% for the rest of his mortgage. Assume there are no additional fees. For simplicity, assume annual mortgage payment. Please show all your work.

a.) What was Brian’s annual mortgage payment?

b.) If he took the refinance opportunity, what is his new annual mortgage payment?

Do not use Excel, please. Need to make calculations.

Answer 1

a)
Loan	$200,000.00
Rate	8.00%
Nper	25	years
Annual payment = $200,000/PVOA (8%,25)
Annual payment = $200,000/10.67478	$18,735.75
b)
Period	Annual Payment	Interest = previous yr reduction in prin. val. x 8%	Principal = Annual payment - interest	Reduction in principal
0				$200,000.00
1	$18,735.75	$16,000.00	$2,735.75	$197,264.25
2	$18,735.75	$15,781.14	$2,954.61	$194,309.64
3	$18,735.75	$15,544.77	$3,190.98	$191,118.66
4	$18,735.75	$15,289.49	$3,446.26	$187,672.41
5	$18,735.75	$15,013.79	$3,721.96	$183,950.45
6	$18,735.75	$14,716.04	$4,019.71	$179,930.74
7	$18,735.75	$14,394.46	$4,341.29	$175,589.45
8	$18,735.75	$14,047.16	$4,688.59	$170,900.86
9	$18,735.75	$13,672.07	$5,063.68	$165,837.17
10	$18,735.75	$13,266.97	$5,468.78	$160,368.40
Balance remain at end of 10th year	$160,368.40
Rate	5.00%
Nper	15
Annual Payment = $160,368/PVOA(5%,15)
Annual Payment = $160,368/10.37966	$15,450.26