Question

You purchase a home for $120,000. You obtain a 30 year loan from Bank Second, paying 20% down, with your loan to be paid off in monthly payments.

a. If the annual interest rate is 8.5% and your first payment is in February, what is your outstanding principal balance after your April payment?

b. ​How much interest would you save by obtaining a 15 year loan versus a 30 year loan? Show all work.

Answer 1

Purchase of Home = $120,000

Down Payment @20% = $24,000

30- Year Bank Loan = $96,000

Interest Rate = 8.5%

Calculation of Monthly Payments

Bank Loan = $96,000

PVAF(8.5%/12, 360 periods) = 129.8143

Monthly Payments = $96000/129.8143

= $739.52 (Approx)

a. Calculation of Outstanding balance after April Payment

Schedule of Payments for One year

Period	Period of Payment	Opening Balance	Monthly Payment	Principal	Interest	Closing Balance
1	Februrary	$           96,000.00	$                 -738.16	$ -58.16	$-680.00	$         95,941.84
2	March	$           95,941.84	$                 -738.16	$ -58.57	$-679.59	$         95,883.27
3	April	$           95,883.27	$                 -738.16	$ -58.98	$-679.17	$         95,824.29
4	May	$           95,824.29	$                 -738.16	$ -59.40	$-678.76	$         95,764.89
5	June	$           95,764.89	$                 -738.16	$ -59.82	$-678.33	$         95,705.07
6	July	$           95,705.07	$                 -738.16	$ -60.25	$-677.91	$         95,644.82
7	August	$           95,644.82	$                 -738.16	$ -60.67	$-677.48	$         95,584.15
8	September	$           95,584.15	$                 -738.16	$ -61.10	$-677.05	$         95,523.05
9	October	$           95,523.05	$                 -738.16	$ -61.54	$-676.62	$         95,461.51
10	November	$           95,461.51	$                 -738.16	$ -61.97	$-676.19	$         95,399.54
11	December	$           95,399.54	$                 -738.16	$ -62.41	$-675.75	$         95,337.13
12	January	$           95,337.13	$                 -738.16	$ -62.85	$-675.30	$         95,274.28

Therefore we from the above the outstanding principal balance after April month payment is $95,824.29.

b.

Calculation of monthly payments if the loan is for 15 years

Bank Loan = $96,000

PVAF(8.5%/12, 180 periods) = 101.4289

Monthly Payments = $96000/101.4289

= $946.48 (Approx)

Total Amount payable if loan is for 15 years = $946.48*180

= $170,366.40

(-) Principal     = $96,000

Interest = $74,366.40

Total Amount payable if loan is for 30 years = $738.16*360

= $265,777.60

(-) Principal     = $96,000

Interest = $169,737.60

By obtaining 15 year loan we can save an interest of = $169,737.60-$74,366.40

= $95,371.20