Final answer:
To calculate the remaining balance on a $150,000 mortgage after 36 payments with an interest rate of 8% compounded monthly, the Future Value formula for an ordinary annuity is used, with the monthly payment determined first by an annuity present value formula. The monthly interest rate is determined, monthly payment is calculated, and then the remaining balance is found by using the number of payments made in the Future Value formula.
Step-by-step explanation:
The remaining balance on a $150,000 mortgage after 36 payments with a nominal interest rate of 8% (compounded monthly) over 30 years can be calculated using the amortization formula. To find the remaining balance, we can use the formula for the Future Value of an ordinary annuity since the mortgage payment constitutes an annuity. The formula for the Future Value (FV) of an ordinary annuity is FV = P * [(1 + r)^n - 1] / r, where P is the monthly payment, r is the monthly interest rate, and n is the number of payments made.
First, we need to calculate the monthly payment. We begin by converting the annual nominal rate to a monthly rate by dividing by 12, giving us 0.08/12 = 0.0066667. Then, using the ordinary annuity present value formula, P = A / [(1 - (1 + r)^-nt) / r], where A is the loan amount ($150,000), n is the total number of payments (360), and t is the time period after which we want the balance (36 months), we solve for P.
Once we have P, we use it to compute the remaining balance using the FV formula, replacing n with the number of payments already made (36) and subtracting this from the original loan amount.