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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?

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Edufirst
Percentage of Total value of Adele’s account of the total value of Leela’s account = [Va / Vl]*100

Vl = 500 * (1.045)t
Va = 500 * (1.045) (t+2)  [this is an amendment of your equation]

[Va/ Vl]*100 = [500 * (1.045)(t+2)] / [500 * (1.045)t]*100= [t+2]*100 / t

[Va/ Vl]*100= [100t + 200] / t = 100 + 200 /t

The first year, t = 1: 100 + 200/1 = 300 %

After two years, t = 2: 100 + 200/2 = 200%

After three years, t = 3: 100 + 200/3 = 167 %

Answer:

109.20% ( approx )

Step-by-step explanation:

Given,

Leela's total investment after t years,

[tex]V_l=500(1.045)^t[/tex]

Also, Adele's investment after t years,

[tex]V_a=500(1.045)^{t+2}[/tex]

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

[tex]=\frac{500(1.045)^{t+2}}{500(1.045)^t}\times 100[/tex]

[tex]=\frac{500(1.045)^{t}(1.045)^2}{500(1.045)^t}\times 100[/tex]

[tex]=(1.045)^2\times 100[/tex]

[tex]=109.2025\%[/tex]

[tex]\approx 109.20\%[/tex]

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