Question

You want to buy a car. The loan amount will be $35,000. The company is offering a 5% interest rate for 36 months (3years). What will your monthly payments be?

Answer 1

Given that:

`\begin{gathered} \text{Loan amount, P}_0=35000 \\ \text{Annual interst rate, r = }5\%=0.05 \\ \text{Number of compounding periods in one year, k =12} \\ L\text{ength of loan(in years), N = 3} \end{gathered}`

Find the monthly payment, d.

The formula to find the monthly payment is

`P_0=(d(1-(1+(r)/(k))^(-Nk)))/(((r)/(k)))`

Plug the given values into the formula.

`\begin{gathered} 35000=(d(1-(1+(0.05)/(12))^(-3\cdot12)))/(((0.05)/(12))) \\ =33.3657d \\ d=(35000)/(33.3657) \\ =1048.98 \end{gathered}`

The monthly payment is $1049 approximately.