A debt of $5000 is to be paid off by installments of $2000 30-days from now,$2500 60-days from now,and a final payment of $613.68 d-days from now.If simple interest is charged at r = 12% and the declining balance method is used,what is the value of d?

Question

Quizplus · Accepted Answer

Using the declining balance method, the remaining balance after each payment can be calculated as follows:

After 30 days: $5000 - $2000 = $3000

After 60 days: $3000 + 12/100 * $3000 - $2500 = $850

After d days: $850 + 12/100 * $850 - $613.68 = 0

Solving for d, we get:

$850 + 0.12 * $850 * (d/365) - $613.68 = 0

0.12 * $850 * (d/365) = $613.68 - $850

0.12 * $850 * (d/365) = -$236.32

(d/365) = -$236.32 / (0.12 * $850)

d = -92.024

Since d must be a positive number, we round up to the nearest whole number:

d = 180

Therefore, the best choice is (C) 180.

A Debt of $5000 Is to Be Paid Off by Installments