What is the balance after one month for a loan amount of $100,000 over 15 years at an interest rate of 6%?

To find the balance after one month for a loan amount of $100,000 over 15 years at an interest rate of 6%, it is essential to calculate the monthly payment and then determine how much of the principal is left after the first month of payments.

First, the loan's term is 15 years, which equals 180 months. The monthly interest rate is calculated by dividing the annual rate by 12, so 6% annually translates to 0.5% monthly (6% / 12 = 0.5%).

Using the formula for a fixed-rate mortgage payment: [ M = P \frac{r(1+r)^n}{(1+r)^n - 1} ] where:

• M is the monthly payment,
• P is the principal (loan amount),
• r is the monthly interest rate (as a decimal),
• n is the number of payments (total months).

Plugging in the values:

• P = $100,000,
• r = 0.005 (0.5% as a decimal),
• n = 180.

Calculating the monthly payment results in approximately $843.86.

Next, the interest for the first month is calculated as: [ \