Math Problem Statement

Kurt paid ₱130,000 as a down payment for a car. The remaining amount is to be settled by paying ₱26,547.57 monthly for five years. If the interest is 12.5% compounded monthly, what is the cash price of the car?

Solution

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Problem: The cash value or cash price of a purchase is equal to the down payment (if there are any) plus the present value of the installment payment.

Example 4: Kurt paid #130,000 as a down payment for a car. The remaining amount is to be settled by paying at the end of each month #26,547.57 for five years. If the interest rate is 12.5% compounded monthly, what is the cash price of the car?

Solution Outline:

To solve this, we can use the present value formula for an annuity, since Kurt will make equal monthly payments over five years:

The present value PVPV of an annuity is given by:

PV=P×1(1+r)nrPV = P \times \frac{1 - (1 + r)^{-n}}{r}

Where:

  • PP is the monthly payment (#26,547.57),
  • rr is the monthly interest rate (12.5% annual interest compounded monthly, so r=12.5%12=0.0104167r = \frac{12.5\%}{12} = 0.0104167),
  • nn is the total number of payments (5 years × 12 months = 60 months).

The total cash price of the car is the sum of the down payment and the present value of the installment payments.

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Math Problem Analysis

Mathematical Concepts

Present Value of Annuities
Compound Interest
Finance Mathematics

Formulas

PV = P × (1 - (1 + r)^-n) / r
Total Cash Price = Down Payment + Present Value of Payments

Theorems

Annuity Present Value Formula

Suitable Grade Level

Grade 11-12 or College