Final answer:
The question involves using an amortization formula to calculate the number of months required to pay off a loan of $32,500 at a 6.50% interest rate compounded monthly with monthly payments of $1,500. This requires rearranging the standard loan formula and solving for the number of payments.
Step-by-step explanation:
To determine how long it will take to settle a loan of $32,500 with a 6.50% interest rate compounded monthly and monthly payments of $1,500, we must utilize the amortization formula. This requires setting up the formula to solve for the number of monthly payments, often denoted as 'n'.
The loan amortization formula with additional payments can be adjusted from the example given:
PV = R * [1 - (1+i)^-n] / i
Where:
- PV is the Present Value or initial loan amount ($32,500)
- R is the monthly payment ($1,500)
- i is the monthly interest rate (6.50% annual rate / 12 months)
- n is the number of months to pay off the loan
We can rearrange the formula to solve for 'n':
n = -log(1 - i * PV / R) / log(1 + i)
Using these calculations, a direct answer to the original question will be calculated. The exact answer depends on the specific numbers plugged into this equation. This assists in the understanding of the time required to pay off a loan with compound interest when regular payments are made.