Question

Caroline puts $400 into a savings account that earns 6% annually. Write a function that represents this situation, where t is the time in years. Solve algebraically after how many years she will get $1200 in her account (round it to the nearest year).

Answer 1

Answer: 19 years

Explanation:

Given

Amount invested
`\$400`

Rate of interest
`R=6\%`

after 1-year amount becomes

`A=400\left (1+6\%\right)\\A=400\left (1+0.06\right)\\A=400* 1.06\\A=\$424`

After n years it is

`A=400\left (1.06\right)^n`

Sum accumulated is
`\$1200`

`\Rightarrow 1200=400\left(1.06\right)^n\\\Rightarrow 3=\left(1.06\right)^n\\\text{Taking log both sides}\\\Rightarrow n=(\ln 3)/(\ln 1.06)\\\\\Rightarrow n=18.85\approx 19\ \text{years}`