Final answer:
To calculate the regular payment amount for a mortgage loan, the loan amount, interest rate, and term are used with the provided formula. The loan with the larger total cost can be identified by comparing the total payments over the life of the loan. Making additional payments can significantly reduce the time and total cost.
This correct answer is none of the above.
Step-by-step explanation:
To determine the regular payment amount of a mortgage loan and compare the total cost, we can use the formula PV = R [1 - (1 + i)^(-nt)] / i, where PV is the present value of the loan (the amount borrowed), R is the regular payment amount, i is the interest rate per period, n is the number of periods per year, and t is the number of years.
To calculate the monthly payment for Example A:
- Amount borrowed (PV): $1,000,000
- Nominal annual interest rate (r): 6%
- Number of periods per year (n): 12 (monthly)
- Number of years (t): 30
To calculate the interest rate per period, divide the annual rate by the number of periods: i = r/n, which gives us i = 6% / 12 = 0.005 (or 0.5%). We can then substitute the values into the formula to find R, rounding to the nearest dollar.
For Example B:
- Amount borrowed (PV): $300,000
- Nominal annual interest rate (r): 6%
- Number of periods per year (n): 12 (monthly)
- Number of years (t): 30
Following the same steps with these values, we can solve for the regular payment amount R. To explore the scenario of making an extra payment per year, we simply calculate the payments as though there were 13 periods in a year. Then, to find out the time and money saved, we compare the total cost of the loan with 12 and 13 payments per year.
Through comparison, the loan with the larger total cost can be determined. By analyzing the interest and payments over the life of the loan, we see the impact of different interest rates and payment schedules on the total cost of a mortgage.
This correct answer is none of the above.