Twenty-five years ago Sandy invested $3,000. Fifteen years ago she put another $2,000 into the investment. Over the 25 years, interest has accumulated at a rate of 6% compounded monthly. How much interest has she earned over the 25 years?

Question

Quizplus · Accepted Answer

To calculate the total interest earned, we need to calculate the future value of each investment separately and then sum them up, subtracting the initial investments to find the total interest earned. For the first investment of $3,000 made 25 years ago:- Using the formula for compound interest: A = P(1 + r/n)^(nt)- P = $3,000, r = 6% or 0.06, n = 12 (compounded monthly), t = 25- A = 3000(1 + 0.06/12)^(12*25) = 3000(1 + 0.005)^(300) ≈ $13,143.08For the second investment of $2,000 made 15 years ago:- P = $2,000, r = 6% or 0.06, n = 12, t = 15- A = 2000(1 + 0.06/12)^(12*15) = 2000(1 + 0.005)^(180) ≈ $5,160.16Total amount = $13,143.08 + $5,160.16 = $18,303.24Total interest earned = Total amount - Total initial investments = $18,303.24 - ($3,000 + $2,000) = $18,303.24 - $5,000 = $13,303.24The closest answer is E) $13,303, acknowledging a slight rounding difference in the final calculation.

Twenty-Five Years Ago Sandy Invested $3,000