A loan was taken out on March 3,2010 at a simple interest rate of 8%.Interest is to be calculated using ordinary interest (Banker's rule).The amount repaid in 6 months is $12,482.67.What was the original amount of the loan?
A)$11,992.32
B)$11,998.77
C)$12,002.57
D)$12,003.83

Question

Quizplus · Accepted Answer

The ordinary interest (Banker's rule) uses a 360-day year to calculate interest. The formula for simple interest is $I = P \times r \times t$, where $I$ is the interest, $P$ is the principal amount (the original loan amount), $r$ is the annual interest rate, and $t$ is the time in years. Given an 8% interest rate, a repayment amount of $12,482.67 after 6 months, we need to find $P$.First, convert the interest rate to a decimal: 8% = 0.08.Next, calculate the time in years: 6 months = $\frac{6}{12}$ = 0.5 years.The total amount repaid includes the original loan amount plus the interest, so $P + I = \$12,482.67$.Using the formula for simple interest, we can substitute $I = P \times r \times t$ into the total repayment equation to get $P + P \times r \times t = \$12,482.67$.Plugging in the values, we get $P + P \times 0.08 \times 0.5 = \$12,482.67$.Simplifying, $P \times (1 + 0.08 \times 0.5) = \$12,482.67$.Further simplifying, $P \times 1.04 = \$12,482.67$.Solving for $P$, we get $P = \frac{\$12,482.67}{1.04} = \$11,992.32$.

A Loan Was Taken Out on March 3,2010 at a Simple