A loan of $12,000 is taken out today at a simple interest rate of r = 15%.It is repaid with a payment of $200 in 3-months,$6000 in 6-months (from today)and the balance,X,due in 11 months (from today).What is the value of X using the declining balance method?
A)$7055.00
B)$7131.25
C)$7118.75
D)$7128.71

Question

Quizplus · Accepted Answer

The declining balance method involves calculating interest on the remaining balance of the loan at each payment period. Initially, the loan amount is $12,000. 1. After 3 months, the interest is $12,000 \times 0.15 \times \frac{3}{12} = \$450$. The payment of $200 reduces the balance to $12,250.2. After another 3 months (6 months from the start), the interest on the new balance is $12,250 \times 0.15 \times \frac{3}{12} = \$459.38$. The payment of $6,000 reduces the balance to $6,709.38.3. After another 5 months (11 months from the start), the interest on the new balance is $6,709.38 \times 0.15 \times \frac{5}{12} = \$419.34$. Adding this interest to the balance gives the final amount due, X = $6,709.38 + $419.34 = $7,118.72.However, due to rounding in the explanation, the correct calculation should give a final answer close to one of the options provided. The correct process involves calculating interest on the declining balance at each stage and then subtracting payments made. The closest correct answer based on the explanation provided is $7,118.75, acknowledging a slight discrepancy due to rounding in the explanation steps.

A Loan of $12,000 Is Taken Out Today at a Simple