Step 1: Calculate the interest costs from the previous year (Year 10).
This part of the question involves separating the principal and interest components of your loan repayments. The first thing we need to calculate is the monthly repayment over the course of the loan. The information required for this computation is summarised below:
Summary Information: Original Loan
Original Loan Amount (PV)
150,000 – 15,000 = 135,000
Monthly Repayment (a)
Monthly Interest Rate (i)
0.07% (the annual rate divided by 12)
Number of Repayments (n)
300 (25 years of monthly repayments)
To compute the amount of the monthly repayment, set the present value of the series of repayments (an annuity) equal to the amount borrowed:
in which case the monthly repayment, a, is $1,078.
The interest paid over the tenth year of the loan can be calculated by comparing the total repayments for that year to the reduction in principal of the loan between the start and end of the year. We know that the repayments of a loan comprise both a principal and an interest component so the interest costs can be calculated as total repayments – reduction in principal.
The reduction in principal over the tenth year is the difference between the balance outstanding at the end of the ninth year and the balance outstanding at the end of the tenth year. The principal outstanding at the end of nine years is determined by computing the present value of all remaining repayments at that time:
The principal outstanding at the…