Question

Tyler begins funding a college education fund for his son. He saves $1000 the first year. Each year he saves 5% more than the previous year. How much money will be in the college education fund at the end of 18 years?

Answer 1

I’m sorry I don’t know it

Answer 2

In the first year Tyler saves $1000

In the second year Tyler will save 5% more than what he saved in the first year and that can be represented as:

`1000+(5)/(100)* 1000=1000+0.05 * 1000=1000(1+0.05)=1000* 1.05`

Thus, we see that the ratio of the second year's savings to first year's savings is 1.05. Please note that this ratio will continue because Tyler will save 5% more than the previous year as given in the question. Therefore, this represents a case of geometric series where the first term,
`a_1=1000`, the common ratio,
`r=1.05` and the number of terms (the total number of years Tyler will save),
`n=18`.

Now, to find Tyler's total savings, we will simply use the sum formula for a geometric series which is:

`S_n=a_1((r^n-1)/(r-1))`

In our case,
`S_n` is:

`S_(18)=1000(((1.05)^(18)-1)/(1.05-1))\approx1000* 28.132=28132`

Thus, the money that will be in the college education fund at the end of 18 years is $ 28,132 (approx).