Question

zoom picture, please

Troy Juth wants to purchase new dive equipment for Underwater Connection, his retail store in Colorado Springs. He was offered a $53,000 loan at 6% for 60 months. What is his monthly payment by formula? (Round your answer to the nearest cent.) Monthly payment

Answer 1

Here, the payments will be same every month, so it is an annuity. For calculating the present value of annuity, we will use the following formula:

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

where, PVA = Present value of annuity = $53000, P is the monthly amount , r is the rate of interest = 6%, so,monthly rate = 6% / 12 = 0.5% and n is the time period = 60 months

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

$53000 = P * (1 - (1 + 0.5%)^-60 / 0.5%)

$53000 = P * (1 - ( 1+ 0.005)^-60 / 0.005)

$53000 = P * (1 - ( 1.005)^-60 / 0.005)

$53000 = P * (1 - 0.74137219624) / 0.005)

$53000 = P * (0.25862780376 / 0.005)

$53000 = P * 51.725560752

P = $53000 / 51.725560752

P = $1024.64

So, monthly payments = $1024.64