Question

Suppose you want a mortgage for $350,000 for 30 years, monthly payments but you cannot currently afford the contract rate of 8.5%. The seller offers to buy down your contract rate to 5% the first year and 6.5% the second year. What are the payments for the first three years if you do this?

Answer 1

To find the monthly payments for the first three years of a mortgage with a principal of $350,000 and varying interest rates, the loan payment formula is applied. The monthly interest rates for the first year (5%), second year (6.5%), and third year (assuming 8.5%) are used with the principal to calculate payments, not including additional costs like insurance.

Step-by-step explanation:

To calculate the monthly payments for the first three years of a mortgage with a principal of $350,000 and varying interest rates, we must use the formula for the monthly payment of a fixed-rate amortizing loan:

P = [rPv] / [1 - (1 + r)^{-n}]

Where:

• P is the monthly payment
• r is the monthly interest rate (annual interest rate divided by 12)
• Pv is the present value, which is the principal amount
• n is the number of payments to be made

For the first year, the interest rate is 5%, for the second year, it's 6.5%, and for the third year let's assume it returns to the original contracted rate of 8.5%. Also, let's take note that the interest rate is compounded monthly.

First Year (5%):

r = 5% / 12 months = 0.004167 per month
Pv = $350,000
n = 30 * 12 (since it's a 30-year mortgage)

The calculation yields a monthly payment for the first year. Repeat this process with the rates for the second and third year.

Note: This calculation doesn't include considerations like property taxes, insurance, and mortgage insurance which could affect the actual monthly payment.