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:
[tex] 1000+\frac{5}{100}\times 1000=1000+0.05 \times 1000=1000(1+0.05)=1000\times 1.05 [/tex]
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, [tex] a_1=1000 [/tex], the common ratio, [tex] r=1.05 [/tex] and the number of terms (the total number of years Tyler will save), [tex] n=18 [/tex].
Now, to find Tyler's total savings, we will simply use the sum formula for a geometric series which is:
[tex] S_n=a_1(\frac{r^n-1}{r-1}) [/tex]
In our case, [tex] S_n [/tex] is:
[tex] S_{18}=1000(\frac{(1.05)^{18}-1}{1.05-1})\approx1000\times 28.132=28132 [/tex]
Thus, the money that will be in the college education fund at the end of 18 years is $ 28,132 (approx).
