Question

A mortgage broker is offering a $284,000 20-year mortgage with a teaser rate. In the first two years of the mortgage, the borrower makes monthly payments on only a 5.0 percent APR interest rate. After the second year, the mortgage interest rate charged increases to 8.0 percent APR.

What are the monthly payments in the first two years? What are the monthly payments after the second year

Answer 1

Asn 1) will use PV of annuity formula

PV of annuity = payment * (1 - (1+r)^-n)/r

where r = 5%/12

n = 20* 12 = 240

PV of annuity = $284000

Payment = $ 1874.27

Amortization schedule for two month is given below:

SO we can find the closing balance end of two year

Month	Opening Balance	Payment	Interest	Principal Payment	Closing Balance
1	$        284,000.00	$ 1,874.27	$ 1,183.33	$                 690.94	$     283,309.06
2	$        283,309.06	$ 1,874.27	$ 1,180.45	$                 693.82	$     282,615.24
3	$        282,615.24	$ 1,874.27	$ 1,177.56	$                 696.71	$     281,918.53
4	$        281,918.53	$ 1,874.27	$ 1,174.66	$                 699.61	$     281,218.91
5	$        281,218.91	$ 1,874.27	$ 1,171.75	$                 702.53	$     280,516.39
6	$        280,516.39	$ 1,874.27	$ 1,168.82	$                 705.46	$     279,810.93
7	$        279,810.93	$ 1,874.27	$ 1,165.88	$                 708.40	$     279,102.53
8	$        279,102.53	$ 1,874.27	$ 1,162.93	$                 711.35	$     278,391.19
9	$        278,391.19	$ 1,874.27	$ 1,159.96	$                 714.31	$     277,676.88
10	$        277,676.88	$ 1,874.27	$ 1,156.99	$                 717.29	$     276,959.59
11	$        276,959.59	$ 1,874.27	$ 1,154.00	$                 720.28	$     276,239.31
12	$        276,239.31	$ 1,874.27	$ 1,151.00	$                 723.28	$     275,516.04
13	$        275,516.04	$ 1,874.27	$ 1,147.98	$                 726.29	$     274,789.74
14	$        274,789.74	$ 1,874.27	$ 1,144.96	$                 729.32	$     274,060.43
15	$        274,060.43	$ 1,874.27	$ 1,141.92	$                 732.36	$     273,328.07
16	$        273,328.07	$ 1,874.27	$ 1,138.87	$                 735.41	$     272,592.66
17	$        272,592.66	$ 1,874.27	$ 1,135.80	$                 738.47	$     271,854.19
18	$        271,854.19	$ 1,874.27	$ 1,132.73	$                 741.55	$     271,112.64
19	$        271,112.64	$ 1,874.27	$ 1,129.64	$                 744.64	$     270,368.01
20	$        270,368.01	$ 1,874.27	$ 1,126.53	$                 747.74	$     269,620.27
21	$        269,620.27	$ 1,874.27	$ 1,123.42	$                 750.86	$     268,869.41
22	$        268,869.41	$ 1,874.27	$ 1,120.29	$                 753.99	$     268,115.42
23	$        268,115.42	$ 1,874.27	$ 1,117.15	$                 757.13	$     267,358.30
24	$        267,358.30	$ 1,874.27	$ 1,113.99	$                 760.28	$     266,598.02

Ans b) Closing balance end of two year = $266598

Monthly payment after second year is given by following formula

where r = 8%/12 = .67%  

n = 216

payment = $2332.63