Question

Louis has an obligation to pay a sum of r7000,00 four years from now. his creditor permits him to discharge the debt by paying r2000,00 one year from now and a final payment of x three years from now. the interest rate charged on all amounts is 11% per year, compounded quarterly. this is represented by the following timeline with the debt above the line and the payments below the line: topic 4.4 q14 the value of x is equal to _________.

a. r4485,83.
b. r3784,33.
c. r3842,11.
d. r3795,40.

Answer 1

To find the value of x for Louis's debt payment plan, the present value of obligation and payments are calculated using the present value formula considering an 11% annual interest rate compounded quarterly. The final payment, x, is then deduced from the balance after accounting for the earlier payment.

Step-by-step explanation:

In order to determine the value of x, which represents the final payment Louis needs to make three years from now to discharge his debt, considering an interest rate of 11% per year, compounded quarterly, we start by calculating the present value of Louis's obligation of R7000 due four years from now. To do this, we use the formula for the present value of a single sum, Present Value = Future Value / (1 + r/n)nt, where r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years. First, we find the present values of Louis's obligation and his payment of R2000 due one year from now. Next, we use the present value of R7000 to find the future value of the debt at the end of three years. Subtract the present value of the R2000 payment from this amount to find the balance that must be settled with the final payment, x. Finally, x can be calculated by applying the present value formula to solve for the future value that equates to this remaining balance.