Question

Facts:

There is a home you want to purchase with a selling price of $220,000. You have saved $42,000 for a down payment. The bank charges 2 points on the balance of the note (before taking fees into account) in exchange for a 3% rate. The bank also charges financing fees of $800. You request that the fees and points be added to the balance of the mortgage, which the bank agrees to.

Required:

Based on the preceding facts, prepare an amortization table for the mortgage assuming a 30 year note, and another amortization table assuming a 15 year note. Assume you take the loan out on July 1, 2020, and the first payment is due July 31, 2020. For each note, calculate the effective interest rate assuming the note is held to maturity.

Answer 1

Solution:-

1. Amortization Table

There is mentioned that the bank charges 2 points which means one point gets you .25 percent off the mortgage rate and costs the borrower 1 percent of the total mortgage amount.

Therefore, the annual rate will be =3-0.25-0.25=2.5%.

And the cost of points will be= (220,000-42,000)*2%

= $3,560

It is also mentioned that the amount of points and fees will be added to the balance of the mortgage, therefore the balance mortgage amount = 220000-42000+3560+800

= $182,360

Amortization table for 30 years notes for the loan amount $182,360:-

Years	Payment	Principal	Interest	Balance
1	$8,712.73	$4,153.73	$4,559.00	$ 178,206.27
2	$8,712.73	$4,257.57	$4,455.16	$ 173,948.70
3	$8,712.73	$4,364.01	$4,348.72	$ 169,584.68
4	$8,712.73	$4,473.11	$4,239.62	$ 165,111.57
5	$8,712.73	$4,584.94	$4,127.79	$ 160,526.63
6	$8,712.73	$4,699.56	$4,013.17	$ 155,827.06
7	$8,712.73	$4,817.05	$3,895.68	$ 151,010.01
8	$8,712.73	$4,937.48	$3,775.25	$ 146,072.53
9	$8,712.73	$5,060.92	$3,651.81	$ 141,011.61
10	$8,712.73	$5,187.44	$3,525.29	$ 135,824.17
11	$8,712.73	$5,317.13	$3,395.60	$ 130,507.04
12	$8,712.73	$5,450.05	$3,262.68	$ 125,056.99
13	$8,712.73	$5,586.31	$3,126.42	$ 119,470.68
14	$8,712.73	$5,725.96	$2,986.77	$ 113,744.72
15	$8,712.73	$5,869.11	$2,843.62	$ 107,875.61
16	$8,712.73	$6,015.84	$2,696.89	$ 101,859.77
17	$8,712.73	$6,166.24	$2,546.49	$   95,693.53
18	$8,712.73	$6,320.39	$2,392.34	$   89,373.14
19	$8,712.73	$6,478.40	$2,234.33	$   82,894.74
20	$8,712.73	$6,640.36	$2,072.37	$   76,254.37
21	$8,712.73	$6,806.37	$1,906.36	$   69,448.00
22	$8,712.73	$6,976.53	$1,736.20	$   62,471.47
23	$8,712.73	$7,150.94	$1,561.79	$   55,320.53
24	$8,712.73	$7,329.72	$1,383.01	$   47,990.81
25	$8,712.73	$7,512.96	$1,199.77	$   40,477.85
26	$8,712.73	$7,700.78	$1,011.95	$   32,777.07
27	$8,712.73	$7,893.30	$819.43	$   24,883.76
28	$8,712.73	$8,090.64	$622.09	$   16,793.13
29	$8,712.73	$8,292.90	$419.83	$     8,500.22
30	$8,712.73	$8,500.22	$212.51	$             0.00

Amortization table for 15 years notes for the loan amount $182,360:-

Years	Payment	Principal	Interest	Balance
1	$14,728.57	$10,169.57	$4,559.00	$ 172,190.43
2	$14,728.57	$10,423.81	$4,304.76	$ 161,766.62
3	$14,728.57	$10,684.41	$4,044.17	$ 151,082.21
4	$14,728.57	$10,951.52	$3,777.06	$ 140,130.70
5	$14,728.57	$11,225.30	$3,503.27	$ 128,905.39
6	$14,728.57	$11,505.94	$3,222.63	$ 117,399.46
7	$14,728.57	$11,793.58	$2,934.99	$ 105,605.87
8	$14,728.57	$12,088.42	$2,640.15	$   93,517.45
9	$14,728.57	$12,390.63	$2,337.94	$   81,126.82
10	$14,728.57	$12,700.40	$2,028.17	$   68,426.41
11	$14,728.57	$13,017.91	$1,710.66	$   55,408.50
12	$14,728.57	$13,343.36	$1,385.21	$   42,065.15
13	$14,728.57	$13,676.94	$1,051.63	$   28,388.20
14	$14,728.57	$14,018.87	$709.71	$   14,369.34
15	$14,728.57	$14,369.34	$359.23	$                 -

(Note: The amortization table is calculate on the yearly basis.)

2. Effective Interest rate:

Formula:-

Effective Rate = (1 + Nominal Rate / n)^n - 1

Nonimal rate= Annual rate charge by the bank i.e 2.5%

n= Compound period i.e 12 months as it is mentioned in the question.

Effective interest rate=  (1+ 0.025/12)^12 -1

= 0.02528 i.e 2.528%

Therefore, Effective interest rate for 30 years note = (1+0.02528)^30 -1

= 111.48%

and Effective interest rate for 15 years note = (1+0.02528)^15 -1

= 45.42%