If a loan of $30,000 is obtained and calls for the principal to be paid in equal monthly installments over 25 years at an interest rate of 0.75% per month, what is the amount of the first payment?

To determine the amount of the first payment on a loan of $30,000 with a monthly interest rate of 0.75% over 25 years, you would use the formula for calculating the monthly payment on an amortized loan.

The formula for the monthly payment (M) is given by:

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

Where:

• M is the monthly payment,
• P is the loan principal ($30,000 in this case),
• r is the monthly interest rate (0.75% or 0.0075 when expressed as a decimal),
• n is the total number of payments (25 years × 12 months = 300 payments).

Substituting the given values into the formula, we get:

1. Convert the monthly interest rate from a percentage to a decimal: 0.75% = 0.0075.

2. Calculate the number of payments: 25 years × 12 months/year = 300 months.

3. Plug the values into the formula:

   [ M = 30000 \frac{0.0075(1 + 0.007