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:

$1000+\frac{5}{100}\times 1000=1000+0.05 \times 1000=1000(1+0.05)=1000\times 1.05$

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:

$S_n=a_1(\frac{r^n-1}{r-1})$

In our case, $S_n$ is:

$S_{18}=1000(\frac{(1.05)^{18}-1}{1.05-1})\approx1000\times 28.132=28132$

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