A loan of $10,000 was taken out at a simple interest rate of 12%.The first two partial payments are: $200 (91 days after the loan date)and $Y (39 days later).Using the declining balance method,the loan balance immediately after the payment of Y is $8228.67.What is the value of Y?
A)$2198.73
B)$2002.56
C)$2000.00
D)$1998.73

Question

Quizplus · Accepted Answer

Using simple interest, we can find the total interest charged over the life of the loan:
I = Prt = 10,000 * 0.12 * (130/365) = $539.45

So the total amount owed at the end of 130 days (91 + 39) is:
A = 10,000 + 539.45 = $10,539.45

Using the declining balance method, the balance after the first payment of $200 is:
B1 = 10,000 * (1 + 0.12 * (91/365)) − 200 = $9,456.60

Then, the balance after the second payment of Y is:
B2 = B1 * (1 + 0.12 * (39/365)) − Y = $8,228.67

Setting this equal to the given value, we have:
8,228.67 = 9,456.60 * (1 + 0.12 * (39/365)) − Y
Y = 1998.73

Therefore, the best choice is D: $1998.73.

A Loan of $10,000 Was Taken Out at a Simple