Question

You are buying a car and will borrow $23,167 with a 5-year loan. The interest rate is 4.44%, what is your monthly payment? Enter only numbers and decimals in your response. Round to 2 decimal places. Use your financial calculator 100% 16

Answer 1

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

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

where, PVA = Present value of annuity = $23167, P is the periodical amount, r is the rate of interest = 4.44% compounded monthly, so monthly rate = 4.44% / 12 = 0.37% and n is the time period = 5 * 12 = 60 months

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

$23167 = P * (1 - (1 + 0.37%)^-60 / 0.37%)

$23167 = P * (1 - ( 1+ 0.0037)^-60 / 0.0037)

$23167 = P * (1 - ( 1.0037)^-60 / 0.0037)

$23167 = P * (1 - 0.80124355836) / 0.0037)

$23167 = P * (0.19875644163 / 0.0037)

$23167 = P * 53.7179571977

P = $23167 / 53.7179571977

P = $431.27

So, monthly payments are $431.27