Reflecting on Investment Accounts: Adele and Leela

What is the total value of Adele's account compared to Leela's account?

a. 101.3%

b. 104.5%

c. 109.0%

d. 109.2%

Final answer:

To determine the percentage of Adele's account value compared to Leela's, we calculate the ratio of their future values using the simple interest formula. Adele's account value is approximately 108.9% of Leela's at that time.

Explanation:

To find the total value of Adele's account as a percentage of Leela's account at any time t, we can compare the future values of their investments using the simple interest formula. Leela invests $500 at 4.5% interest, so her account value after t years is given by Vl = 500(1 + 0.045t).

Adele invests the same amount at the same interest rate but starts two years earlier, so her account value after t years is Va = 500(1 + 0.045(t-2)).

To determine the percentage of Adele's account value compared to Leela's, we need to calculate the ratio Va / Vl. Substituting the equations above, we get (500(1 + 0.045(t-2))) / (500(1 + 0.045t)).

Simplifying this expression, we find the ratio to be (1 + 0.045(t-2)) / (1 + 0.045t).

At any given time t, we can substitute the value of t into the ratio expression to find the percentage.

For example, if we substitute t = 4 (which means 4 years have passed), the ratio becomes (1 + 0.045(4-2)) / (1 + 0.045(4)) = 1.089.

This means Adele's account value is approximately 108.9% of Leela's at that time.