A loan of $5000 is taken out on May 25.The interest rate on the loan is r = 12%.A payment of $105 is made 102 days later and a payment of X,is due 175 days after May 25.What is X if the declining balance method is used?
A)$5180.15
B)$5182.67
C)$5184.18
D)$5287.67

Question

Quizplus · Accepted Answer

Using the declining balance method, the interest for the first 102 days is:
$5000 x 12%/365 days x 102 days = $167.12
Therefore, after the first payment of $105, the remaining balance is:
$5000 + $167.12 - $105 = $5062.12
The interest for the next 73 days is:
$5062.12 x 12%/365 days x 73 days = $124.55
So the amount owed after the second payment is:
$5062.12 + $124.55 - X = $4936.67 - X
Using the formula for the present value of a loan with equal payments, we can set up the equation:
$5000 = (105/1.12) + (X/1.12)^2/(1.12+1.12^2+...+1.12^n-1)
Where n is the number of periods between the first and second payments (175 days - 102 days = 73 days)
Solving for X, we get:
X = $5182.67

A Loan of $5000 Is Taken Out on May 25