Question

Tina wants to save money for school. Tina invests 400 in an account that pays an interest rate of 8%How many years will it take for the account to reach 5,500? Round your answer to the nearest hundredth

Answer 1

Given the amount invested as 400 with an interest rate of 8%, the number of years it takes to reach 5,500 is calculated as

Thus,

`\begin{gathered} A=5500 \\ P=400 \\ r=8\text{\%}=(8)/(100)=0.08 \\ t\text{ is unkown} \end{gathered}`

Substituting the parameters in the equation, we have

`\begin{gathered} 5500=400(1+0.08)^t \\ (5500)/(400)=1.08^t \\ 13.75=1.08^t \end{gathered}`

Taking the logarithm of both sides to base 10, we have

`\begin{gathered} \log _(10)(13.75)=\log _(10)(1.08)^t \\ 1.1383=t*0.0334 \\ t=(1.1383)/(0.0334)=34.081 \end{gathered}`

Thus, it will take 34.08 years (nearest hundredth) to reach 5,500.