Final answer:
The student wants to know the maximum loan amount they can borrow, given a monthly payment ability of $359 over 48 months at a 6% APR, compounded monthly. The calculation involves the present value of an annuity formula with the specified payment amount, interest rate, and number of periods.
Step-by-step explanation:
The student is asking about the maximum loan amount that can be borrowed given the condition of being able to afford $359 monthly payments for 48 months at an APR of 6%, compounded monthly. To calculate this, we utilize the present value of an annuity formula, which considers the regular payment amount, the number of payments, and the interest rate.
To find the maximum amount Karl can borrow, we must determine the present value of an annuity based on the given monthly payment (PMT), number of periods (n), and the monthly interest rate (i). The formula to be used is:
PV = PMT × · · ((1 - (1 + i)^-n) / i)
In this scenario, PMT is $359, n is 48, and i is 0.5% per month (which is 0.005 in decimal form). Plugging in these values, we calculate the present value, which represents the loan amount Karl can borrow. The calculated amount will be the maximum loan that Karl can afford to take out under the given repayment conditions.