Question

Leela invests $500 at 4.5% interest according to the equation VI=500(1.045)t, where Vl is the value of the account after t years. Adele invests the same amount of money at the same interest rate, but begins investing two years earlier according to the equation Va=500(1.045)t+2. The total value of Adele’s account is approximately what percent of the total value of Leela’s account at any time, t?

Answer 1

109.20% ( approx )

Explanation:

Given,

Leela's total investment after t years,

`V_l=500(1.045)^t`

Also, Adele's investment after t years,

`V_a=500(1.045)^(t+2)`

Hence, the percentage of total value of Adele’s account to the total value of Leela’s account at any time, t
`=\frac{\text{Adele's investment after t years}}{\text{Leela's total investment after t years}}* 100`

`=(500(1.045)^(t+2))/(500(1.045)^t)* 100`

`=(500(1.045)^(t)(1.045)^2)/(500(1.045)^t)* 100`

`=(1.045)^2* 100`

`=109.2025\%`

`\approx 109.20\%`