### Math Notes

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#### Algebra Solutions

##### Topics || Problems

A man invests 500 dollars at the end of each year for 16 years at 5% simple interest. What is the accumulated value of his investments just after the 16th investment. if no interest has been withdrawn.

This problem simulate an arithmetic series:

End of First year -- 500

End of Second year -- 500 +25

End of Third year -- 500 +50

...

500, 525, 550, ...

$$a_{16} = 500+25(15)$$

$$a_{16} = 875$$

$$s_{16} = \frac{16}{2} (500+875)$$

$$s_{16} = 11~000$$

The accumulated value of the investment after 16 years is 11, 000 dollars