MONTHLY PAYMENT
The formula to calculate the monthly payment is given to be:
[tex]A=P\cdot\frac{r(1+r)^n}{(1+r)^n-1}[/tex]
where
[tex]\begin{gathered} A=\text{ Monthly payment} \\ P=\text{ Loan amount} \\ r=\text{ }Interest\text{ rate per period} \\ n=\text{ }Total\text{ number of periods} \end{gathered}[/tex]
From the provided question, we have the following parameters:
[tex]\begin{gathered} P=3400 \\ r=\frac{0.162}{12}=0.0135 \\ n=48\text{ months} \end{gathered}[/tex]
Therefore, we can calculate the monthly payment to be:
[tex]\begin{gathered} A=3400\times\frac{0.0135(1+0.0135)^{48}}{(1+0.0135)^{48}-1} \\ A=96.71 \end{gathered}[/tex]
The monthly payment is $96.71
INTEREST PAID
The interest paid can be calculated as the difference between the loan amount and the total amount repaid:
[tex]Interest=\text{ Amount Repaid - Loan Amount}[/tex]
If the payment monthly is $96.71, the amount paid over 48 months will be:
[tex]\Rightarrow96.71\times48=4642.08[/tex]
Therefore, the interest paid will be:
[tex]Interest=4642.08-3400=1242.08[/tex]
The interest paid is $1,242.08
