Question

The Small Business Administration offers business loans at 5.55% interest compounded monthly for 6 years. If the owner of a restaurant can afford monthly payments of $750, what is the maximum amount the owner can borrow?

Answer 1

To find the maximum loan amount, we need to use the formula for the future value of an ordinary annuity. The formula is PMT = (PV * r) / (1 - (1+r)^(-n)).

Step-by-step explanation:

To find the maximum loan amount, we need to use the formula for the future value of an ordinary annuity. The formula is: PMT = (PV * r) / (1 - (1+r)^(-n)), where PMT is the monthly payment, PV is the present value (maximum loan amount), r is the interest rate per period, and n is the number of periods. We know that the monthly payment (PMT) is $750, the interest rate (r) is 5.55% divided by 12 (since it's compounded monthly), and the number of periods (n) is 6 years multiplied by 12 (since it's compounded monthly).

Substituting the known values into the formula: 750 = (PV * (0.0555/12)) / (1 - (1 + (0.0555/12))^(-6*12)).

Solving this equation will give us the maximum loan amount (PV).