Ordinary Annuity

Question

Nicole bought a car with the cash value of P15,294 on the installment plan under the following terms: P4,312 cash upon delivery and the balance payable in 12 equal monthly payments. Assuming money is worth 5.23% compounded quarterly. How much is his remaining debt at the end of eight months?

Answer 1

Hi Madison!

In order to tackle this question we first have to see what we are given. We are given that the cars total value is $15,294 and the down payment of the car is $4,312. This means that we have a total remaining value of $10,982 left to pay on the car ($15,294 - $4,312).

We are given that the balance is payable in 12 months and that the remaining balance is compounded at a rate of 5.23% quarterly. This means that the number of times the 5.23% is compounded is 4 times. In order to see the total value left to pay off the car at the end of one year we can use the equation: Car Loan Left (1 + rate) ^ (number of years * times compounded in a year). Using this we get a total of $13,466 ($10,982 * (1.0523)^4). We have a total of $13,466 that needs to be paid in a year.

The question is asking how much debt we have after 8 months - this means that we paid off 8 months of the debt. Each month we will pay $13,466/12 = $1,122. $1,122 * 8 = $8,977 that we have paid after 8 months. The remaining value that we will have left to pay is $13,466 - $8,977 = around $4,489. This is how much we have left at the end of 8 months to pay. Please reach out if you have any question with the explanation!