Question

Sabrina has decided to invest her savings in real estate. 20 months ago, she purchased a duplex for $800,000. She could afford to make a down-payment of $50,000. The bank gave her a 30-year mortgage with constant monthly payments at a quoted APR of 12% with semi-annual compounding. Today, (after making her last monthly payment to the bank) Sabrina was able to resell her property for $815,000. With the money she has left after paying the bank for the remaining mortgage, Sabrina will make a down-payment on a new property. What is the down-payment she can make on this new property? Hint: First find the monthly payments she must make.

a. $73,922.57
b. $60,718.76
c. $45,320.68
d. $70,026.35
e. $58,026.36

Answer 1

Answer : d. $70,026.35

Complete calculations below :

Loan Amount = Property value - Down Payment = 800,000 - 50,000 = $750,000

Life of loan = 30 years

Rate of interest = APR 12% compounded semi annually

Calculations :

Interest per month =   $7,547.91

Therefore, total payment in 20 months = 7,547.91*20 = 150,958.20

Balance at the end of 20 months :

	Beginning Balance	Interest	Principal	Ending Balance
1	$750,000.00	$7,319.10	$228.81	$749,771.19
2	$749,771.19	$7,316.86	$231.04	$749,540.15
3	$749,540.15	$7,314.61	$233.30	$749,306.85
4	$749,306.85	$7,312.33	$235.57	$749,071.28
5	$749,071.28	$7,310.03	$237.87	$748,833.40
6	$748,833.40	$7,307.71	$240.19	$748,593.21
7	$748,593.21	$7,305.37	$242.54	$748,350.67
8	$748,350.67	$7,303.00	$244.91	$748,105.77
9	$748,105.77	$7,300.61	$247.30	$747,858.47
10	$747,858.47	$7,298.20	$249.71	$747,608.76
11	$747,608.76	$7,295.76	$252.15	$747,356.62
12	$747,356.62	$7,293.30	$254.61	$747,102.01
Year #1 End
13	$747,102.01	$7,290.81	$257.09	$746,844.92
14	$746,844.92	$7,288.31	$259.60	$746,585.32
15	$746,585.32	$7,285.77	$262.13	$746,323.19
16	$746,323.19	$7,283.21	$264.69	$746,058.50
17	$746,058.50	$7,280.63	$267.27	$745,791.22
18	$745,791.22	$7,278.02	$269.88	$745,521.34
19	$745,521.34	$7,275.39	$272.52	$745,248.82
20	$745,248.82	$7,272.73	$275.18	$744,973.65

Amount required to pay off the loan in full = 744973.65 (assuming no other cost)

Amount from sale = 815,000

Balance= 815,000 - 7,44,973.65 = 70,026.35