Question

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the car you are interested in costs $18,000. you have saved up $2,000
for a downpayment and are looking to finance the rest. your bank offers a
4.5% car loan to be repaid over 60 months.
what would your monthly payment be?
choose 1 answer:
a $37.29
b $298.29
c $335.57
d $372.86

Explanation:

Step1: Determine the loan amount

The car costs $18,000 and the downpayment is $2,000. So the loan amount $PV$ is $18000 - 2000 = 16000$.

Step2: Identify the interest rate and period

The annual interest rate $r$ is 4.5% or 0.045. Since it's a monthly payment, the monthly interest rate $i$ is $\frac{0.045}{12}$. The number of months $n$ is 60.

Step3: Use the loan payment formula

The formula for the monthly payment $M$ of a loan is $M = PV\times\frac{i(1 + i)^n}{(1 + i)^n - 1}$.
First, calculate $i=\frac{0.045}{12}=0.00375$.
Then, calculate $(1 + i)^n=(1 + 0.00375)^{60}$. Let's compute $(1.00375)^{60}\approx1.251795$.
Next, calculate the numerator: $i(1 + i)^n = 0.00375\times1.251795\approx0.004694$.
The denominator: $(1 + i)^n - 1=1.251795 - 1 = 0.251795$.
Now, $M = 16000\times\frac{0.004694}{0.251795}\approx16000\times0.01864\approx298.29$.

Answer:

B. $298.29$