Question

(4) A payment of $X two years from now along with a payment of $2X four years from now repays a debt of $6,000 at 6.5% annual effective compound interest. Find X.

Answer 1

Answer:

$1,618.49

Explanation:

The compound interest on $X for 2 years and add to the compound interest of $2X for 4 years, equals $6,000

      FV = P(1+r)^n + P(1+r)^n

$6,000 = X(1+6.5%)^2 + 2X(1+6.5%)^4

$6,000 = X(1+0.065)^2 + 2X(1+0.065)^4

$6,000 = X(1.065)^2 + 2X(1.065)^4

$6,000 = X(1.134225) + 2X(1.286466351)

$6,000 = 1.134225X + 2.572932701X

$6,000 = 3.707157701X

Divide both sides by 3.707157701

$6,000/3.707157701 = 3.707157701X/3.707157701

          $1618.490629 = X

                   $1,618.49 = X

                                X = $1,618.49