12. A buyer is purchasing a $400,000 home and the lender has approved a $320,000 mortgage with a 6% interest rate, amortized over 30 years. What will the buyer's yearly principal and interest payments total (rounded up)? (BE SURE TO USE THE AMORTIZATION TABLE.)
Answer: C
The buyer's yearly principal and interest payments will total $29,867.
To calculate the yearly principal and interest payments for the mortgage, we use the mortgage amount of $320,000, the interest rate of 6%, and the amortization period of 30 years. This results in an annual payment of approximately $29,867.
A) 23,248
This option is incorrect as it underestimates the total yearly payments. A mortgage of $320,000 at a 6% interest rate over 30 years results in higher payments than this figure when calculated using an amortization schedule.
B) 29,060
While this option is closer to the correct figure, it still does not account for the full payment required at the specified interest rate and term. The correct calculation using the mortgage formula yields a total that exceeds this amount.
C) 29,867
This option is correct. It accurately reflects the total yearly principal and interest payments derived from the amortization of a $320,000 mortgage at a 6% interest rate over 30 years, confirming that the calculation aligns with standard mortgage payment formulas.
D) 34,874
This option is incorrect as it significantly overestimates the yearly payments. The calculation for a $320,000 mortgage at 6% over 30 years produces a total payment well below this amount, indicating that this choice does not fit the financial parameters provided.
Conclusion
The correct answer of $29,867 is supported by the proper application of the mortgage payment formula using the given loan amount, interest rate, and amortization period. Other options either underestimate or overestimate the required payments, demonstrating a failure to accurately apply the calculation for this mortgage scenario.