A home buyer obtains a fully amortized loan of $140,000. What is the payment difference between a 15-year loan at 5% and a 30-year loan at 6%?

To find the payment difference between a 15-year loan at 5% and a 30-year loan at 6%, we first need to understand how to calculate monthly mortgage payments using the loan amount, interest rate, and term.

For a fully amortized loan, the formula to determine the monthly payment is:

[ M = P \times \frac{r(1 + r)^n}{(1 + r)^n - 1} ]

where:

• ( M ) is the total monthly mortgage payment,
• ( P ) is the loan principal (the amount borrowed),
• ( r ) is the monthly interest rate (annual rate divided by 12),
• ( n ) is the number of payments (loan term in months).

1. Calculating the Payment for the 15-Year Loan at 5%:
   • Principal: $140,000
   • Annual Interest Rate: 5% → Monthly Interest Rate: 0.05 / 12 = 0.0041667
   • Term: 15 years → 15 x 12 = 180 months

Using the formula: [ M_{15} = 140,000 \times \frac{0.