Final answer:
To determine how long it will take Brandon to pay off the loan of $20,000 with an annual interest rate of 4.2%, compounded monthly, and monthly payments of $250, we can use the formula for the present value of an annuity. Plugging in the values, it will take Brandon approximately 97.4 months, or 8.1 years, to pay off the loan.
Step-by-step explanation:
To determine how long it will take Brandon to pay off the loan, we can use the formula for the present value of an annuity:
Loan amount = Payment amount × ((1 - (1 + interest rate/number of periods)-number of periods × time))/ (interest rate/number of periods)
In this case, the loan amount is $20,000, the payment amount is $250, the interest rate is 4.2% (or 0.042), and the number of periods is 12 (compounded monthly). The formula can be rearranged to solve for time:
Time = (log((payment amount × interest rate/number of periods)/ (loan amount × interest rate/number of periods - payment amount))+1) / (log(1 + interest rate/number of periods))
Plugging in the values, we find that it will take Brandon approximately 97.4 months, or 8.1 years, to pay off the loan.