Question

Larry Davis borrows $76,000 at 12 percent interest toward the purchase of a home. His mortgage is for 30 years. Use Appendix D for an approximate answer, but calculate your final answer using the formula and financial calculator methods. a. How much will his annual payments be?

How much interest will he pay over the life of the loan?

How much should he be willing to pay to get out of a 12 percent mortgage and into a 10 percent mortgage with 30 years remaining on the mortgage? Assume current interest rates are 10 percent. Carefully consider the time value of money. Disregard taxes.

Answer 1

Answer A) Loan amortisation at 12% for 30*12= 360 months for the borrowing of $76000

using formula in excel = PMT(12%/12,360,-76000,0,1)

Loan Principle Amount		76,000.00
Annual Interest Rate		12.00%
Loan Period (in months)		360.00
Original Repayment Amount(monthly)		781.75

His annual payments be = 781.75 * 12 = $ 9381

Answer B)

The complete calculation of loan will be as below:

Repayment Number	Opening Balance	Loan Repayment	Interest Charged	Capital Repaid	Closing Balance
1	$76,000.00	$781.75	$760.00	$21.75	$75,978.25
2	$75,978.25	$781.75	$759.78	$21.96	$75,956.29
3	$75,956.29	$781.75	$759.56	$22.18	$75,934.11
4	$75,934.11	$781.75	$759.34	$22.40	$75,911.70
5	$75,911.70	$781.75	$759.12	$22.63	$75,889.08
6	$75,889.08	$781.75	$758.89	$22.85	$75,866.22
…………………..
357	$3,050.34	$781.75	$30.50	$751.24	$2,299.10
358	$2,299.10	$781.75	$22.99	$758.75	$1,540.35
359	$1,540.35	$781.75	$15.40	$766.34	$774.01
360	$774.01	$781.75	$7.74	$774.01	$0.00
	Total	$281,428.41	$205,428.41	$76,000.00

Total Interest paid = $ 205428.41

Answer ) in case of 10 % loan calculation will be

Loan Principle Amount		76,000.00
Annual Interest Rate		10.00%
Loan Period (in months)		360.00
Original Repayment Amount(month)		666.95

Annual payment = 12 * 666.95 = $8003.45

Per year Saving to switch in 10% from 12% =  $ 9381 - $8003.45=$1377.55

Total Benefit = PV ( $1377.55 for 30 years @ 10%)

Benefit = $12985.10 , as calculated below

years	Benefits	PV( Benefit)
1	$1,377.45	$1,252.23
2	$1,377.45	$1,138.39
3	$1,377.45	$1,034.90
4	$1,377.45	$940.82
5	$1,377.45	$855.29
6	$1,377.45	$777.53
7	$1,377.45	$706.85
8	$1,377.45	$642.59
9	$1,377.45	$584.17
10	$1,377.45	$531.07
11	$1,377.45	$482.79
12	$1,377.45	$438.90
13	$1,377.45	$399.00
14	$1,377.45	$362.73
15	$1,377.45	$329.75
16	$1,377.45	$299.77
17	$1,377.45	$272.52
18	$1,377.45	$247.75
19	$1,377.45	$225.22
20	$1,377.45	$204.75
21	$1,377.45	$186.14
22	$1,377.45	$169.21
23	$1,377.45	$153.83
24	$1,377.45	$139.85
25	$1,377.45	$127.13
26	$1,377.45	$115.58
27	$1,377.45	$105.07
28	$1,377.45	$95.52
29	$1,377.45	$86.83
30	$1,377.45	$78.94
	Total benfits	$12,985.10