Final answer:
Nancy will repay a total of $29,648.14 on her $24,000 loan from the State Bank after 2 years and 3 months, based on an annual compound interest rate of 10%.
Step-by-step explanation:
The subject in question deals with the calculation of compound interest. Nancy needs to find out the payment she will have to make after 2 years and 3 months on a $24,000 loan from the State Bank at an interest rate of 10% per annum compounded annually. To calculate this, we will use the formula for compound interest which is A = P(1 + r/n)(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years.
In Nancy's case, P = $24,000, r = 10% or 0.10, n = 1 since the interest is compounded annually, and t = 2.25 years (since 3 months is a quarter of a year). Plugging these values into the formula, we get A = $24,000(1 + 0.10/1)(1*2.25). When we calculate this, it yields Nancy's total payment due to the bank after 2 years and 3 months.
Nancy will have to pay a total of $29,648.14 on her $24,000 loan after 2 years and 3 months at a 10% annual compound interest rate.