Question

Rupesh wants to buy a new BMW priced at $54,000. He makes a down payment of 20% of the original price. He also trades-in his old car for $10,000. (This means he sells the old car to the dealer for $10,000). For the balance, Rupesh takes a 60-month car loan at an interest rate of 3.45%. What will be the approximate payment at the end of every month

Answer 1

The approximate payment at the end of every month will be $603.22.

Step-by-step explanation:

Since the payment is going to be made at the end of every month, this can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (1)

Where;

PV = Present value or the balance = Price of BMW - Down payment - Old car sales amount = $54,000 - ($54,000 * 20%) - $10,000 = $33,200

P = Monthly payment = ?

r = Monthly interest rate = Annual interest rate / 12 = 3.45% / 12 = 0.0345 /

12 = 0.002875

n = number of months = 60

Substitute the values into equation (1) and solve for P, we have:

$33,200 = P * ((1 - (1 / (1 + 0.002875))^60) / 0.002875)

$33,200 = P * 55.0377058660197

P = $33,200 / 55.0377058660197

P = $603.22

Therefore, the approximate payment at the end of every month will be $603.22.