How to work out the cumulative compound interest of something over a set period?

Question

For example: If I want to get to a total of 1,500 in 30 increments. Each time the base value increases by 5%.

For example

Increment	Value	Total
1	10	10
2	10.5	20.5
3	11.025	31.525
...	...	...
30	...	1500

How do I work out what the initial value is to get a total of 1500 after 30 5% increases (compounding)?

Answer 1

It is unclear whether you are adding an extra amount each time on top of the compound interest. I assume not in what follows

Hints:

• Each increment involves multiplying by $1.05$

• $30$ increments involves multiplying $30$ times by $1.05$, i.e. by $1.05^{30}$. How much is this?

• What number do you need to multiply by $1.05^{30}$ to get $1500$?

If you are adding an extra amount $x$ each time then you need to adjust this, with what amounts to a geometric series