Answer:
Please check the explanation below.
Explanation:
Rate of Interest =10% or 0.83% monthly
Monthly Payment under this plan=PMT(0.0083, 360, 300000) =$2,632.71
Loan outstanding after 5 years of payments =$289,723
New Interest Rate =8.5% or 0.7083% monthly
Balance Tenure= 25 years
New Monthly Installment =PMT(0.007083,300,289723) =$2,332.93
Monthly savings in installment reduction =$2,632.71 - 2,332.93 =$299.78
a. Net present value of refinancing = -0.05x289,723 + 299.78x{(1-(1+0.007083)-300)/0.007083}
= -14,486.15 + 299.78x124.1886
= -14,486.15 + 37,229.25
= 22,743.10
b. With new monthly installment, balance outstanding at the end of 8th year =$278,258
Net Present Value of Refinance = -0.05x289,723 + 299.78x{(1-(1+0.007083)-36)/0.007083}
= -14,486.15 + 299.78x31.68
= -14,486.15 + 9,446.46
= -4,989.68
c. For refinance loan to have net present value positive, let n payments are required,
NPV = -0.05x289,723 + 299.78x{(1-(1+0.007083)-n)/0.007083}
14,486.15 = 299.78x{(1-(1+0.007083)-n)/0.007083}
14,486.15x0.00783/299.78 =(1-(1.007083)-n)
0.3423 = 1-(1.007083)-n
(1.007083)-n = 0.6577
(1.007083)n = 1.5204
Taking Log both sides,
n = log(1.5204)/log(1.007083)
n = 59.36
Hence, he would need to make 60 payments for making NPV of refinance as zero.
