SOLUTION: Tyler's dad starts a college fund and saves 1000.00 the first year and each year he saves 5% more than the previous year. How much money would be in the college fund at the end of
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Question 1076511: Tyler's dad starts a college fund and saves 1000.00 the first year and each year he saves 5% more than the previous year. How much money would be in the college fund at the end of 18 years?
Thank you for you help!
Jordan Found 3 solutions by jorel1380, josmiceli, MathTherapy:Answer by jorel1380(3719) (Show Source):
You can put this solution on YOUR website! Let 1000.00 be the initial deposit. Then the next year, Tyler's dad deposits 1050.00, or 1000(1.05)^1. The next year, he deposits 1050(1.05), or 1000 x (1.05)^2. So Tyler has 1000 (1.05)^0 + 1000 (1.05)^1 + 1000(1.05)^2..... which equals 1000 x Σ(1.05)^n, with n from 0 to 18. This amounts to 1000 x 30.539, which equals $30539.00 at the end of 18 years. ☺☺☺☺
You can put this solution on YOUR website! After the 1st year, you have:
The 2nd year you have:
Then the 3rd year you have:
If you get this next step, then you get the whole thing.
Factor out
-------------------------
And if you repeat this for 18 years, you get:
$2,292.02 saved after 18 years
Feel free to get a 2nd opinion on this
You can put this solution on YOUR website! Tyler's dad starts a college fund and saves 1000.00 the first year and each year he saves 5% more than the previous year. How much money would be in the college fund at the end of 18 years?
Thank you for you help!
Jordan
This scenario represents a GEOMETRIC series, with a 1st term, or of 1,000, and a common ratio, or “r” of 1 +.05, or 1.05
Each term of a GEOMETRIC series:
18th term of this series:
Formula for sum of a GEOMETRIC series:
Sum of the 18 terms/years-savings of this series, or:
