What is the total amount of interest earned between the end of 18 months and the end of 36 months on an investment of $1000 if the interest rate is j₁₂ = 9%? A)$308.65 B)$164.69 C)$154.94 D)$143.96

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Quizplus · Accepted Answer

The interest earned between the end of 18 months and the end of 36 months can be calculated using the formula for compound interest: A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), 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. Given that the interest rate is 9% (or 0.09 as a decimal), and assuming the interest is compounded annually (n = 1), for the first 18 months (1.5 years), the formula becomes: A1 = 1000(1 + 0.09/1)^(1*1.5) = 1000(1.09)^1.5. For the next 18 months to reach 36 months (another 1.5 years), we calculate the interest on the amount A1, so the formula for the total amount A2 at the end of 36 months is: A2 = A1(1 + 0.09/1)^(1*1.5). The interest earned between the end of 18 months and the end of 36 months is A2 - A1. Calculating A1: A1 = 1000(1.09)^1.5 ≈ 1148.31. Calculating A2: A2 = 1148.31(1.09)^1.5 ≈ 1313.00. The interest earned between the end of 18 months and the end of 36 months is 1313.00 - 1148.31 = $164.69.

What Is the Total Amount of Interest Earned Between the End