Final answer:
The effective annual interest rate for a $1,500 discounted loan at an 8% simple interest rate for 2 years is approximately 9.5% when rounded to the nearest tenth of a percent.
Step-by-step explanation:
To calculate the effective annual interest rate of a discounted loan, we must first understand the terms of the loan. Roger has taken out a $1,500 loan with an 8% simple interest rate for 2 years. A discounted loan means that the interest is deducted from the principal at the beginning, and the borrower receives the net amount.
First, we must find the total interest that will be charged over the life of the loan using the formula for simple interest:
Interest = Principal × rate × time. Therefore, Interest = $1,500 × 0.08 × 2 = $240. This $240 is deducted upfront, and Roger will receive $1,500 - $240 = $1,260 at the beginning of the loan term and will repay $1,500 at the end.
To find the effective annual interest rate, we calculate the annual interest based on the amount received. So for each year, the interest is $240/2 = $120. The effective annual interest rate (r) is therefore $120/$1,260, and to express this as a percentage we multiply by 100, getting approximately 9.52%. So, the effective annual interest rate is 9.5% when rounded to the nearest tenth of a percent.