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?

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 %

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slicergiza slicergiza · Answer 2 · 2019-07-18T01:38:21-04:00

Answer:

109.20% ( approx )

Step-by-step 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 $=\frac{\text{Adele's investment after t years}}{\text{Leela's total investment after t years}}\times 100$

$=\frac{500(1.045)^{t+2}}{500(1.045)^t}\times 100$

$=\frac{500(1.045)^{t}(1.045)^2}{500(1.045)^t}\times 100$

$=(1.045)^2\times 100$

$=109.2025\%$

$\approx 109.20\%$