Answer to Question #199768 in Financial Math for Esaya Chauke

Question

Give your answer to this question correct to the nearest rand. Fisokuhle has a textbook loan that was

supposed to be paid in two payments of R1 637,00 due six months ago and R1 746,00 due in nine months

from now. Instead, he renegotiates to pay R622,00 today and the balance in three months, therefore, the

settlement date is at month three. The debts and payments are subject to the same interest rate of 9% per

annum, compounded quarterly. The value of X, rounded to the nearest rand, is equal to?

Answer 1

$4194.39

Step-by-step explanation:

Two equal payments one after 3 months and another after 9 months respectively are used to settle a debt of $6000 due today.

We have to calculate the size of the equal payments at 9% compounded quarterly.

Let the amount be $x.

So, (x + x) =x+x)=2x will be the total sum after interest.

Therefore, 6000 will be charged for 3 months at 6% interest quarterly and

000willbechargedfor3monthsat6(6000 - x) will be charged for (9 - 3) = 6 months at 6% interest quarterly.

The equation we can write is

⇒ 6000 × 1.06 + ( 6000 - x)(1.1236)2x

⇒ 3.1236x = 6000 × 2.1836

⇒ x = $4194.39 (Answer)