Question

Hannah, Iris, and Jolene each have an investment worth $5,891.22. The details of their investments follow.Hannah: annual interest rate of 14% compounded quarterly for 6 yearsIris: annual interest rate of 7% compounded monthly for 63 monthsJolene: annual interest rate of 9% compounded quarterly for 7 yearsWhich statement about their initial investments is correct?(1 point)ResponsesJolene's initial investment was more than Iris' initial investmentJolene's initial investment was more than Iris' initial investmentHannah's initial investment was the leastHannah's initial investment was the leastIris' initial investment was less than Hannah's initial investmentIris' initial investment was less than Hannah's initial investmentJolene's initial investment was the greatestJolene's initial investment was the greatest

Answer 1

Compute each initial amount P = 5891.22 / (1 + r/m)^(m t):

- Hannah: r = 0.14, m = 4, t = 6 → factor = 1.035^24 ≈ 2.2792 → P ≈ 5891.22 / 2.2792 ≈ $2,585.
- Iris: r = 0.07, m = 12, t = 63/12 = 5.25 → factor = 1.0058333^63 ≈ 1.4428 → P ≈ 5891.22 / 1.4428 ≈ $4,083.
- Jolene: r = 0.09, m = 4, t = 7 → factor = 1.0225^28 ≈ 1.8646 → P ≈ 5891.22 / 1.8646 ≈ $3,160.

Therefore Hannah's initial investment was the least.