Final answer:
To calculate the annual rate of interest on a discounted loan, you need to determine the present value of the loan. In this case, the loan amount is $3,000 and the interest rate is 8%. The annual rate of interest on a discounted loan is 8.01%.
Step-by-step explanation:
To calculate the annual rate of interest if the loan is discounted, you need to determine the present value of the loan. In this case, the loan amount is $3,000, and the interest rate is 8%. Since the loan is discounted, the present value is the amount of money that would need to be invested today to receive the future payment. The formula to calculate the present value of a discounted loan is:
Present Value = Future Value / (1 + (Interest Rate * Time))
Plugging in the values, we get:
Present Value = $3,000 / (1 + (0.08 * 1)) = $2,777.78
Now, to calculate the annual rate of interest, we can use the formula:
Annual Rate = (Future Value - Present Value) / Present Value
Plugging in the values, we get:
Annual Rate = ($3,000 - $2,777.78) / $2,777.78 = 0.0801 or 8.01%