Question

You decide to quit using your credit card and want to pay off the balance of $3,400 in 4 years. Your interest rate is 16.2% compounded monthly.

Answer 1

MONTHLY PAYMENT

The formula to calculate the monthly payment is given to be:

`A=P\cdot(r(1+r)^n)/((1+r)^n-1)`

where

`\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}`

From the provided question, we have the following parameters:

`\begin{gathered} P=3400 \\ r=(0.162)/(12)=0.0135 \\ n=48\text{ months} \end{gathered}`

Therefore, we can calculate the monthly payment to be:

`\begin{gathered} A=3400*(0.0135(1+0.0135)^(48))/((1+0.0135)^(48)-1) \\ A=96.71 \end{gathered}`

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:

`Interest=\text{ Amount Repaid - Loan Amount}`

If the payment monthly is $96.71, the amount paid over 48 months will be:

`\Rightarrow96.71*48=4642.08`

Therefore, the interest paid will be:

`Interest=4642.08-3400=1242.08`

The interest paid is $1,242.08