Question

You would like to buy a house that costs $350,000. You have $50,000 in cash that you can put down on the​ house, but you need to borrow the rest of the purchase price. The bank is offering a​ 30-year mortgage that requires annual payments and has an interest rate of 7% per year. You can afford to pay only $23,500 per year. The bank agrees to allow you to pay this amount each​ year, yet still borrow $300,000. At the end of the mortgage​ (in 30​ years), you must make a balloon​ payment; that​ is, you must repay the remaining balance on the mortgage. How much will this balloon payment​ be?

The PV of the annuity is (Round to the nearest​ dollar.)

The balloon payment is (Round to the nearest​ dollar.)

​$nothing .

​ (Round to the nearest​ dollar.)

Answer 1

Loan Taken = $ 300,000

Yearly Payment = $ 23,500

Year	Opening Bal	Instalment	Int	Principal repay	Closing Bal
1	$ 3,00,000.00	$ 23,500.00	$ 21,000.00	$   2,500.00	$ 2,97,500.00
2	$ 2,97,500.00	$ 23,500.00	$ 20,825.00	$   2,675.00	$ 2,94,825.00
3	$ 2,94,825.00	$ 23,500.00	$ 20,637.75	$   2,862.25	$ 2,91,962.75
4	$ 2,91,962.75	$ 23,500.00	$ 20,437.39	$   3,062.61	$ 2,88,900.14
5	$ 2,88,900.14	$ 23,500.00	$ 20,223.01	$   3,276.99	$ 2,85,623.15
6	$ 2,85,623.15	$ 23,500.00	$ 19,993.62	$   3,506.38	$ 2,82,116.77
7	$ 2,82,116.77	$ 23,500.00	$ 19,748.17	$   3,751.83	$ 2,78,364.95
8	$ 2,78,364.95	$ 23,500.00	$ 19,485.55	$   4,014.45	$ 2,74,350.49
9	$ 2,74,350.49	$ 23,500.00	$ 19,204.53	$   4,295.47	$ 2,70,055.03
10	$ 2,70,055.03	$ 23,500.00	$ 18,903.85	$   4,596.15	$ 2,65,458.88
11	$ 2,65,458.88	$ 23,500.00	$ 18,582.12	$   4,917.88	$ 2,60,541.00
12	$ 2,60,541.00	$ 23,500.00	$ 18,237.87	$   5,262.13	$ 2,55,278.87
13	$ 2,55,278.87	$ 23,500.00	$ 17,869.52	$   5,630.48	$ 2,49,648.39
14	$ 2,49,648.39	$ 23,500.00	$ 17,475.39	$   6,024.61	$ 2,43,623.78
15	$ 2,43,623.78	$ 23,500.00	$ 17,053.66	$   6,446.34	$ 2,37,177.44
16	$ 2,37,177.44	$ 23,500.00	$ 16,602.42	$   6,897.58	$ 2,30,279.87
17	$ 2,30,279.87	$ 23,500.00	$ 16,119.59	$   7,380.41	$ 2,22,899.46
18	$ 2,22,899.46	$ 23,500.00	$ 15,602.96	$   7,897.04	$ 2,15,002.42
19	$ 2,15,002.42	$ 23,500.00	$ 15,050.17	$   8,449.83	$ 2,06,552.59
20	$ 2,06,552.59	$ 23,500.00	$ 14,458.68	$   9,041.32	$ 1,97,511.27
21	$ 1,97,511.27	$ 23,500.00	$ 13,825.79	$   9,674.21	$ 1,87,837.06
22	$ 1,87,837.06	$ 23,500.00	$ 13,148.59	$ 10,351.41	$ 1,77,485.65
23	$ 1,77,485.65	$ 23,500.00	$ 12,424.00	$ 11,076.00	$ 1,66,409.65
24	$ 1,66,409.65	$ 23,500.00	$ 11,648.68	$ 11,851.32	$ 1,54,558.32
25	$ 1,54,558.32	$ 23,500.00	$ 10,819.08	$ 12,680.92	$ 1,41,877.41
26	$ 1,41,877.41	$ 23,500.00	$   9,931.42	$ 13,568.58	$ 1,28,308.82
27	$ 1,28,308.82	$ 23,500.00	$   8,981.62	$ 14,518.38	$ 1,13,790.44
28	$ 1,13,790.44	$ 23,500.00	$   7,965.33	$ 15,534.67	$    98,255.77
29	$    98,255.77	$ 23,500.00	$   6,877.90	$ 16,622.10	$    81,633.68
30	$    81,633.68	$ 23,500.00	$   5,714.36	$ 17,785.64	$    63,848.03

PV of ANNuity = CF * PVAF

= $ 23,500 * PVAF(7%,30)

= 23500 * 12.4090

= 291612.5

Ballon Paymnet = 63843.03 ( Lfet over balance in Amortization Table).