Question

You buy a car for $38,000. You agree to a 60-month loan with a monthly interest rate of 0.55 percent. What is your required monthly payment? Multiple Choice $745.29 $764.07 None of these choices are correct. $634.24 $605.54

Answer 1

We can calculate the monthly payment amount using a calculator of using Excel.

Calculating using Excel is very simple, and easy to understand.

We use the PMT formula to find the monthly payment amount.

Here, the formula will be =PMT(0.0055,60,38000,0,0)

It is explained as below:

Given that,

Loan is to be repaid in 60 monthly instalments.

So, 1 period = 1 month

Interest rate per period, Rate is 0.55% = 0.0055

No. of periods, Nper = 60

Amount of Loan, PV = 38000

Balance of loan pending after the last instalment, FV = 0

Type = 0 means that the installment is being paid at the end of the month.

As the loan payments are an outflow, the result of this formula is a negative value.

So, Monthly payment required to be made is $745.29

----------------------------------------------------------------------------------------------------------------------------

Now let's understand how the calculations are made to find the Installment amount using calculator

Monthly Loan payment = Amount / PVIFA

PVIFA is the Present Value Interest Factor of Annuity. As we are making monthly payments of a fixed amount, whose Present Value is $38000. So, we will use PVIFA for 60 months @ 0.55% per month to calculate the monthly loan payment amount

PVIFA = (1 - (1 + r)^-n) / r

Here, r = interest rate per payment period = 0.55% = 0.0055

n = no. of payment periods = 60

So, PVIFA = (1 - (1 + 0.0055)^-60) / 0.0055 = 50.987

Monthly Loan Payment = $38000 / 50.987 = $ 745.29 (Approx.)