Question

2. You decide to vest $100 into a savings account with an interest rate of 2% annually in 2015. The amount of money in your savings account in a given year can be mogeled by the following function. P(t) = 100(10).0076 a. lue P(0) and explain what it means in this context. (2pts) O b. Approximately how many years will it take for the amount of money in yout bank account reach $140? Round your answer to the nearest year Show all work (2pts)

Answer 1

The amount of money in the savings account 't' years after 2015 is given by,

`P(t)=100*(10)^{0.007t^{}}`

Solve for P(0) as,

`P(0)=100*(10)^(0.007*0)=100*10^0=100*1=100`

It means, at the beginning of the tenure, i. e. year 2015, the account had $100 only.

The time taken for the account to have $140 is calculated as,

`\begin{gathered} P(t)=140 \\ 100*(10)^(0.007t)=140 \\ 10^(0.007t)=1.4 \end{gathered}`

Take common logarithms on both sides,

`\begin{gathered} \ln ^{}_(10)10^(0.007t)=\ln _(10)1.4 \\ 0.007t*\ln _(10)10=0.146 \\ 0.007t*1=0.146 \\ t=(0.146)/(0.007) \\ t\approx21 \end{gathered}`

Thus, it will take arount 21 years for the account to have $140.