6. You want to buy a $250,000 house. You have a 20% down payment and can arrange
ID: 3185166 • Letter: 6
Question
6. You want to buy a $250,000 house. You have a 20% down payment and can arrange a 20 year loan for the balance at 65% compounded monthly a) What is the size of your payment? b) After 5 years, how much equity do you have in the house? c) Assuming that the last payment is the same as the first, when you finish paying off the loan, how much interest have you paid? d) Fill in the portion of the amortization schedule given below. Payment amount Interest for Portion to principal (S) Payment number New balance (S) 0 200,000.00 2 4Explanation / Answer
6. Since the downpayment is 20 % of $ 250000 = $ 50000, the amount of loan is $ 250000-$ 50000 = $ 200000.
a). The formula for computing the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is P = L[r(1 + r)n]/[(1 + r)n - 1]. Here, L = 200000, r = 6.5/1200 = 13/2400 and n = 20*12 = 240. Hence P = (200000*13/2400)[(1+13/2400)240] / [(1+13/2400)240 -1] = (13000/12)* 3.656446705/2.656446705 = $ 1491.15. Thus, the monthly payment is $ 1491.15 ( on rounding off to the nearest cent).
b). The formula is used to calculate the remaining loan balance (B) of a fixed payment loan of $ L after p months is
B = L[(1 + r)n - (1 + r)p]/[(1 + r)n – 1]
Here, p = 5*12 = 60. Hence, B = 200000[(1+13/2400)240 -(1+13/2400)60]/ [(1+13/2400)240 -1] = 200000(3.656446705 -1.382817324 )/(2.656446705) = 200000*2.273629381)/(2.656446705) = $ 171178.24. Thus, the equity after 5 years is $ 250000-$ 171178.24. = $ 78821.76.
c). The total repayment is 240* $ 1491.15 = $ 357876. Hence the amount of interest paid is $357876 - $ 200000 = $ 157876.
d). The given table duly filled up is as under:
Payment No.
Payment Amount($)
Interest for the period($)
Portion to Principal($)
New Balance ($)
0
0
0
0
200000.00
1
1491.15
1083.33
407.82
199592.18
2
1491.15
1081.12
410.03
199182.15
3
1491.15
1078.90
412.25
198769.90
4
1491.15
1076.67
414.48
198355.42
B = L[(1 + r)n - (1 + r)p]/[(1 + r)n – 1]
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