Question

You need a loan to purchase new equipment. The loan will be paid off over 8 years with payments made at the end of every quarter. If the stated annual rate is 12% and quarterly payments are 336, what is the loan amount? (Show your answer to the nearest cent. Round your answer to the nearest 2 decimal places. DO NOT round until after all calculations have been completed and you have reached your final answer.)

Answer 1

To find the loan amount, we use the formula for calculating the present value of an annuity. Plugging in the given values, the loan amount is approximately $8133.87.

Step-by-step explanation:

To find the loan amount, we need to use the formula for calculating the present value of an annuity:

PV = R * [1 - (1 + r)^(-n)] / r

Where PV is the loan amount, R is the quarterly payment, r is the quarterly interest rate, and n is the number of quarters.

In this case, the quarterly payment is $336, the quarterly interest rate is 12% divided by 4 (or 3%), and the number of quarters is 8 * 4 = 32.

Plugging in these values into the formula:

PV = $336 * [1 - (1 + 0.03)^(-32)] / 0.03 = $8133.87

Therefore, the loan amount is approximately $8133.87.