Final answer:
The annual payment for year 16 of a $50,000 constant amortization mortgage at 10% for 25 years is $4,000, which is the sum of the annual principal repayment ($2,000) and the interest for year 16 ($2,000).
Step-by-step explanation:
To calculate the annual payment for year 16 of a $50,000 constant amortization mortgage (CAM) at 10% for 25 years, we first need to understand what a CAM entails. With a constant amortization mortgage, the principal repayment component is constant for each period, while the interest component decreases as the outstanding balance of the loan decreases.
Since the loan amount is $50,000 and the loan is to be fully amortized in 25 years, we calculate the annual principal repayment:
Annual Principal Repayment = Total Loan Amount / Loan Term
Annual Principal Repayment = $50,000 / 25 = $2,000
For any given year, the annual payment is the sum of the fixed principal repayment and the interest on the remaining balance. To find the interest for year 16, we must calculate the remaining balance after 15 years of repayments and then apply the interest rate to this amount.
Remaining Balance after 15 years = Initial Loan Amount - (Annual Principal Repayment x 15)
Remaining Balance after 15 years = $50,000 - ($2,000 x 15) = $50,000 - $30,000 = $20,000
Interest for year 16 = Remaining Balance after 15 years x Interest Rate
Interest for year 16 = $20,000 x 10% = $2,000
Therefore, the total annual payment for year 16 of the mortgage would be the sum of the annual principal repayment and the interest for year 16:
Annual Payment for Year 16 = Annual Principal Repayment + Interest for Year 16
Annual Payment for Year 16 = $2,000 + $2,000 = $4,000
Hence, the correct answer is b) $4,000.