Answer :
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
[tex]6000 (1 + \frac{6}{100} )^{1} + (6000 - x)(1 + \frac{6}{100} )^{2} = 2x[/tex]
⇒ 6000 × 1.06 + ( 6000 - x)(1.1236) = 2x
⇒ 3.1236x = 6000 × 2.1836
⇒ x = $4194.39 (Answer)