Question

Question 8 5 pts Find the monthly payment to retire a $7500 loan over 3 years, that requires monthly payments at 4% annual interest, compounded monthly. Solve for the unknown variable to answer the previous question. You do not need to write a dollar sign. Round your final answer to the nearest cent.

Answer 1

Here, the payments will be same every month, so it is an annuity. We will use the present value of annuity formula to calculate the monthly payment:

PVA = P * (1 - (1 + r)^-n / r)

where, PVA = Present value of annuity = $7500, P is the periodical amount, r is the rate of interest = 4% compounded monthly, so monthly rate = 4% / 12 = 0.333% and n is the time period = 3 * 12 = 36 months

Now, putting these values in the above formula, we get,

7500 = P * (1 - (1 + 0.333%)^-36 / 0.333%)

7500 = P * (1 - ( 1+ 0.00333)^-36 / 0.00333)

7500 = P * (1 - ( 1.003333)^-36 / 0.00333)

7500 = P * (1 - 0.88709744526) / 0.003333)

7500 = P * (0.11290255473 / 0.003333)

75000 = P * 33.8711051326

P = 7500 / 33.8711051326

P = 221.43

So, monthly payments are of 221.43.