Question

Forty-eight (48) months ago, James Alfred Charles purchased a $2,750,000 house in Buckhead with no money down (i.e. he borrowed $2,750,000). The interest rate on his 30-year, monthly payment loan was 6.25 percent. For the first 48 months of the loan, James paid twice the normal required payment (for example, if the required payment to pay off the loan in 30 years was $4000 per month, James actually paid $8000 per month, with all excess being applied against the principle balance). Now, James is thinking about downsizing and he would like to know how much equity he has accumulated in his home. Unfortunately, the market value of his home has depreciated by 30 percent over the past 4 years (thus, James can only sell his house today for $1,925,000). Assuming that James made all of his monthly payments (i.e., twice the required amount) on time and assuming that he can sell his house today (i.e., immediately after making his 48th monthly payment) for $1,925,000, how much equity can James Alfred Charles expect to take out of his home? (Note: for this problem, to achieve as precise an answer as possible, round all intermediate calculations – payment, interest rate, N, etc. to a minimum of 4 decimal places).

Answer 1

The normal payment will be = PMT(6.25%/12, 360, 2750000) = $16,932.2230

So Alfred makes a monthly payment of $16,932.2230*2 = $33,864.4460 each month for 48 months. At the end of 48 months the following balances will be left:

Month	Loan balance at start of the month	Monthly payment	Interest	Loan balance at end of the month
1	2,750,000.0000	33,864.4460	14,322.9167	2,730,458.4706
2	2,730,458.4706	33,864.4460	14,221.1379	2,710,815.1625
3	2,710,815.1625	33,864.4460	14,118.8290	2,691,069.5454
4	2,691,069.5454	33,864.4460	14,015.9872	2,671,221.0866
5	2,671,221.0866	33,864.4460	13,912.6098	2,651,269.2504
6	2,651,269.2504	33,864.4460	13,808.6940	2,631,213.4984
7	2,631,213.4984	33,864.4460	13,704.2370	2,611,053.2894
8	2,611,053.2894	33,864.4460	13,599.2359	2,590,788.0792
9	2,590,788.0792	33,864.4460	13,493.6879	2,570,417.3211
10	2,570,417.3211	33,864.4460	13,387.5902	2,549,940.4653
11	2,549,940.4653	33,864.4460	13,280.9399	2,529,356.9592
12	2,529,356.9592	33,864.4460	13,173.7342	2,508,666.2473
13	2,508,666.2473	33,864.4460	13,065.9700	2,487,867.7714
14	2,487,867.7714	33,864.4460	12,957.6446	2,466,960.9700
15	2,466,960.9700	33,864.4460	12,848.7551	2,445,945.2790
16	2,445,945.2790	33,864.4460	12,739.2983	2,424,820.1313
17	2,424,820.1313	33,864.4460	12,629.2715	2,403,584.9568
18	2,403,584.9568	33,864.4460	12,518.6717	2,382,239.1824
19	2,382,239.1824	33,864.4460	12,407.4957	2,360,782.2322
20	2,360,782.2322	33,864.4460	12,295.7408	2,339,213.5269
21	2,339,213.5269	33,864.4460	12,183.4038	2,317,532.4847
22	2,317,532.4847	33,864.4460	12,070.4817	2,295,738.5204
23	2,295,738.5204	33,864.4460	11,956.9715	2,273,831.0458
24	2,273,831.0458	33,864.4460	11,842.8700	2,251,809.4698
25	2,251,809.4698	33,864.4460	11,728.1743	2,229,673.1981
26	2,229,673.1981	33,864.4460	11,612.8812	2,207,421.6333
27	2,207,421.6333	33,864.4460	11,496.9877	2,185,054.1750
28	2,185,054.1750	33,864.4460	11,380.4905	2,162,570.2194
29	2,162,570.2194	33,864.4460	11,263.3866	2,139,969.1600
30	2,139,969.1600	33,864.4460	11,145.6727	2,117,250.3867
31	2,117,250.3867	33,864.4460	11,027.3458	2,094,413.2864
32	2,094,413.2864	33,864.4460	10,908.4025	2,071,457.2429
33	2,071,457.2429	33,864.4460	10,788.8398	2,048,381.6367
34	2,048,381.6367	33,864.4460	10,668.6544	2,025,185.8450
35	2,025,185.8450	33,864.4460	10,547.8429	2,001,869.2419
36	2,001,869.2419	33,864.4460	10,426.4023	1,978,431.1982
37	1,978,431.1982	33,864.4460	10,304.3292	1,954,871.0813
38	1,954,871.0813	33,864.4460	10,181.6202	1,931,188.2555
39	1,931,188.2555	33,864.4460	10,058.2722	1,907,382.0817
40	1,907,382.0817	33,864.4460	9,934.2817	1,883,451.9173
41	1,883,451.9173	33,864.4460	9,809.6454	1,859,397.1167
42	1,859,397.1167	33,864.4460	9,684.3600	1,835,217.0307
43	1,835,217.0307	33,864.4460	9,558.4220	1,810,911.0067
44	1,810,911.0067	33,864.4460	9,431.8282	1,786,478.3888
45	1,786,478.3888	33,864.4460	9,304.5749	1,761,918.5177
46	1,761,918.5177	33,864.4460	9,176.6589	1,737,230.7307
47	1,737,230.7307	33,864.4460	9,048.0767	1,712,414.3614
48	1,712,414.3614	33,864.4460	8,918.8248	1,687,468.7401

Now equity at the end of 48th month = Fair value of the house - loan due

= 1,925,000 - 1,687,468.7401

= $237,531.26