Question

The amount owed on a line of credit after 123 days was $757.89. if the institution charges 5.5% per annum, what amount was originally drawn against the line of credit?

group of answer choices:
a. $749.00
b. $447.10
c. $750.00
d. $744.10
e. $689.10

Answer 1

The original amount drawn against the line of credit was $744.10, which is found by rearranging the simple interest formula and using the total amount, the annual interest rate, and the time the amount was borrowed to calculate the principal.

Step-by-step explanation:

To determine the original amount drawn against the line of credit, we need to calculate the principal using the simple interest formula. The final amount ($757.89) includes the initial principal plus the interest accrued over 123 days at an annual interest rate of 5.5%. The simple interest formula is I = Prt, where I is interest, P is principal, r is the annual interest rate as a decimal, and t is the time in years. Since our interest is compounded annually, we'll have to adjust our time to reflect this.

Time (t) should be 123 days out of 365, approximately 0.3369 years. First, convert the interest rate from a percentage to a decimal: r = 5.5% = 0.055. Then we rearrange the formula to solve for P: P = I / (rt). But we need to find I, which is the total amount minus the principal. Let's call the final amount A. A = P + I => P = A - (P * r * t) => P = A / (1 + r * t). Substituting the given values: P = $757.89 / (1 + 0.055 * 0.3369), P = $757.89 / 1.01899545, which gives us around $744.10. Therefore, the original amount drawn against the line of credit was $744.10.