Question

Don James purchased a new automobile for $20,000. Don made a cash down payment of $5,000 and agreed to pay the remaining balance in 30 monthly installments, beginning one month from the date of purchase. Financing is available at a 24% annual interest rate. (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Use appropriate factor(s) from the tables provided.)

Required: Calculate the amount of the required monthly payment. (Round your final answer to nearest whole dollar amount.)

Answer 1

Total cost of the automobile = $20000

Cash down payment = $5000

Amount financed = $20000 - $5000 = $15000

Here, the payments will be same every month, so it is an annuity. For calculating the monthly payments, we will use the present value of annuity table as per below:

Present value of future cash payments = P * PVA (r% , n Years)

where, PVA (r%, n years) is the present value of $1 annuity at r% for n years.

Given: Present value of future cash payments = $15000, r = rate of interest = 24%, so monthly rate = 24% / 12 = 2%, n = 30 months.

Putting the values in the above formula, we get,

$15000 = P * PVA (2%, 30)

From the table the value of PVA (2%, 30 Years) is 22.3965

Putting this value in the above equation, we get,

$15000 = P * 22.3965

P = $15000 / 22.3965

P = $669.75 or $670.

So, monthly payments are for $670.