Question

Jean-Claude Bubose will be the best man at his friend's wedding. To pay for plane fare, gifts, and other expenses, he took a $1,800 installment loan. The loan is for 12 months at 8% interest with a $156.60 monthly payment. After 8 months, the balance is $615.87 , and he pays off the loan when the next payment is due. a) What is the amount of the final payment? b) How much does he save by paying the loan off early?

Answer 1

First, we need to find the interest. This is given by

$\begin{gathered} \text{Interest}=(\text{ Balance)}\times(Rate)\times(Time) \\ \text{Interest}=(\text{ \ 615.87)}\times(0.08)\times(\frac{1}{12}) \end{gathered}$

which gives

$\text{Interest}=\text{ \ 4.1058}$

a) What is the amount of the final payment?

The final payment is given by

$\begin{gathered} \text{ Final payment = Balance+Interest} \\ \text{ Final payment =}615.87+4.1058 \\ \text{ Final payment =}619.9758 \end{gathered}$

Then, the answer is $619.9758

b) How much does he save by paying the loan off early?​

Since the loan is for 12 months, the total payment is

$\begin{gathered} \text{Total payment=12}\times156.60 \\ \text{Total payment=}1879.20 \end{gathered}$

Therefore, the amount saved is given by

$\begin{gathered} \text{Amount saved = Total payment-Months payed-Final payment} \\ \text{Amount saved = }1879.20-(8\times156.60)-619.9758 \end{gathered}$

which gives

$\begin{gathered} \text{Amount saved = }1879.20-1252.80-619.9758 \\ \text{Amount saved = }6.4242 \end{gathered}$

Therefore, the answer is $6.4242 saved