Loan payment = 255000 - 40000 = 215000
i = 6.9% / 12 = 0.575% per month
a.
T = 15*12 = 180 months
Monthly payment = 215000 * (A/P,0.5775%,180)
= 215000 * 0.00575 * ((1 + 0.00575)^180)/((1 + 0.00575)^180-1)
= 215000 * 0.00575 * ((1.00575)^180)/((1.00575)^180-1)
= 1920.48 (Nearest Cent)
Total interest paid = 1920.48 * 180 - 215000 = 130686.40
b.
T = 20*12 = 240 months
Monthly payment = 215000 * (A/P,0.575%,240)
= 215000 * 0.00575 * ((1 + 0.00575)^240)/((1 + 0.00575)^240-1)
= 215000 * 0.00575 * ((1.00575)^240)/((1.00575)^240-1)
= 1654.01 (Nearest Cent)
Total interest paid = 1654.01 * 240 - 215000 = 181962.40
c.
T = 25*12 = 300 months
Monthly payment = 215000 * (A/P,0.575%,300)
= 215000 * 0.00575 * ((1 + 0.00575)^300)/((1 + 0.00575)^300-1)
= 215000 * 0.00575 * ((1.00575)^300)/((1.00575)^300-1)
= 1505.89 (Nearest Cent)
Total interest paid = 1505.89 * 300 - 215000 = 236767
d.
Let n months are left to pay when half balance is paid off
half balance = 215000 / 2 = 107500
As per given condition
1654.01 * (P/A,0.575%,n) = 107500
(P/A,0.575%,n) = 107500 / 1654.01 = 64.993561
((1 + 0.00575)^n-1)/(0.00575 *(1 + 0.00575)^n) = 64.993561
((1.00575)^n-1)/(0.00575 *(1.00575)^n) = 64.993561
(1.00575)^n - 1 = 64.993561 * (0.00575 *(1.00575)^n)
(1.00575)^n - 1 = 0.373712976 * (1.00575)^n
(1.00575)^n = 1 / (1 - 0.373712976) = 1.59671199
taking log both sides
n = log 1.59671199 / log 1.00575 = 81.6157 months
Months to pay half balance = 240 - 81.6157 = 158.38 months
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