Question

A local finance company quotes a 14 percent interest rate on one-year loans. So, if you borrow $20,000, the interest for the year will be $2,800. Because you must repay a total of $22,800 in one year, the finance company requires you to pay $22,800/12, or $1,900.00, per month over the next 12 months. a. What rate would legally have to be quoted? Annual percentage rate b. What is the effective annual rate? b. What is the effective annual rate?

Answer 1

The quoted interest rate is 14 percent, but the effective annual rate (EAR) considering monthly compounding turns out to be 14.8962%.

Step-by-step explanation:

Calculating the Effective Annual Rate

The quoted interest rate is 14 percent per annum, calculated using simple interest. To find the effective annual rate (EAR), we must account for the effects of monthly payments rather than a single payment at the end of the year. The formula to calculate the EAR, considering monthly compounding, is: (1 + i/n)^n - 1, where i is the nominal interest rate, and n is the number of compounding periods per year. In this case, i=0.14 and n=12. Plugging the values into the formula gives us the EAR.

First, calculate the monthly interest rate: i/n = 0.14/12 = 0.011666...

Then, calculate the EAR: (1 + 0.011666...)^12 - 1 = 0.148962... or 14.8962% when expressed as a percentage.

The effective annual rate is therefore 14.8962%, which accounts for the monthly payment schedule and compound interest.

Answer 2

The legally required rate that would have to be quoted is called the Annual Percentage Rate (APR). The APR in this case would be 12.28%, not 14%. The effective annual rate is the same as the quoted interest rate of 14%.

Step-by-step explanation:

The legally required rate that would have to be quoted is called the Annual Percentage Rate (APR). To calculate the APR, we need to consider the total amount repaid and the repayment period. In this case, you are borrowing $20,000 and repaying a total of $22,800 over one year. So, the APR can be calculated as follows:

APR = (Total interest / Total amount repaid) * (12 / Repayment period)

APR = (2,800 / 22,800) * (12 / 1) = 0.1228 or 12.28%

The effective annual rate is the actual annual interest rate that takes into account the effect of compounding. Since the interest rate in this case is quoted as 14% annually, it already represents the effective annual rate.