Final answer:
It will take approximately 90 months to pay off the loan.
Step-by-step explanation:
To calculate how long it will take to pay off a loan of $45,000 at an annual rate of 10% compounded monthly with monthly payments of $500, we need to use the formula for the number of periods in a loan. The formula is:
n = -log1+r(1-((P*r)/A)) / log1+r
Where:
- n is the number of periods
- P is the loan amount ($45,000)
- r is the monthly interest rate (10% / 12)
- A is the monthly payment ($500)
Calculating this gives us n = 89.67. Since the number of periods must be a whole number, we round up to the nearest whole number. Therefore, it will take approximately 90 months to pay off the loan.