- #1

Rectifier

Gold Member

- 313

- 4

## Homework Statement

Alfred puts 985 USD on his bank account every time he has a birthday. Alfred just turned 48. He started to save money when he turned 35 (including 35th birthday). How much money is there on his savings-account if the interest-rate was 3.7% every year and that he had no money in that account when he started saving.

*This problem was translated from Swedish. Sorry for possible grammatical and typographical errors.*

## Homework Equations

A geometrical sum can be written as:

$$S=\frac{x^{n+1}-1}{x-1}$$

## The Attempt at a Solution

This looks lika a geometrical sum. This is the first problem in the chapter and I am already stuck.

Alfreds deposits (not sure if that's the right word) looked like this:

$$985 + 985 \cdot 1.037^1 + ... + 985 \cdot 1.037^m$$

*I will explai why i wrote m there soon.*

This can be written as:

$$Money = 985(1 +1.037^1 + ... + 1.037^m)$$

**The problem I am having is**the number that I have to put instead of m. Is it 12, 13 or 14 and what happens when I want to calculate the sum? Will the sum be:

$$Money = 985 \cdot S= 985 \cdot \frac{1.037^{m+1}-1}{1.037-1}$$

Please help me :(

**Many thanks in advance!**

Last edited: