Question

a debt of $6000 due today is to be settled by two payments due three months from now and 9 months from now respectively . what is the size of the equal payments at 6% compounded quarterly?​

Answer 1

Answer:

$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 6% compounded quarterly.

Let the amount be $x.

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

Therefore, $6000 will be charged for 3 months at 6% interest quarterly and $(6000 - x) will be charged for (9 - 3) = 6 months at 6% interest quarterly.

The equation we can write is  

$6000 (1 + \frac{6}{100} )^{1} + (6000 - x)(1 + \frac{6}{100} )^{2} = 2x$

⇒ 6000 × 1.06 + ( 6000 - x)(1.1236) = 2x

⇒ 3.1236x = 6000 × 2.1836

⇒ x = $4194.39 (Answer)