# Regular Savings-Geometric Progression Question

**URL:** <https://boards.straightdope.com/t/regular-savings-geometric-progression-question/51210>\
**Category:** Factual Questions\
**Created:** [January 22, 2001, 3:51am UTC](https://boards.straightdope.com/t/regular-savings-geometric-progression-question/51210 "2001-01-22T03:51:38Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![Ell](https://avatars.discourse-cdn.com/v4/letter/e/e47774/32.png) [@Ell](https://boards.straightdope.com/u/Ell)\
**Post date:** [January 22, 2001, 3:51am UTC](https://boards.straightdope.com/t/regular-savings-geometric-progression-question/51210/1 "2001-01-22T03:51:38Z")

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I’m setting up a retirement fund for myself (I’m really planning ahead).

Say I start with $1500 and then add $100 a month at 15% interest, I was just wondering how much money I would have in x amount of years.

I know there are calculators out there that do this but I remember you can do this by geometric progression and would like to do it manually.

Can you give me a hand with the formula?

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**Author:** ![Cabbage](https://avatars.discourse-cdn.com/v4/letter/c/f07891/32.png) [@Cabbage](https://boards.straightdope.com/u/Cabbage)\
**Post date:** [January 22, 2001, 5:08am UTC](https://boards.straightdope.com/t/regular-savings-geometric-progression-question/51210/2 "2001-01-22T05:08:04Z")

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Well, to find how much all your $100 deposits will add up to, you can use this equation for calculating the future value of an annuity (assuming the interest will be compounded monthly). Future Value =

## 100\*(1 + 0.15/12)[sup]12t[/sup] - 100

```
  0.15/12

```

t = number of years.

Can’t forget the original $1500, so we also need to find how much that will be after t years. Future Value =

1500\*(1 + 0.15/12)[sup]12t[/sup]

Add the two together to get the total.

So, for example, after 30 years your annuity will be about $692327.90, your $1500 will have grown to about $131311.48, for a total of $823639.38.

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**Author:** ![Ell](https://avatars.discourse-cdn.com/v4/letter/e/e47774/32.png) [@Ell](https://boards.straightdope.com/u/Ell)\
**Post date:** [January 22, 2001, 5:30am UTC](https://boards.straightdope.com/t/regular-savings-geometric-progression-question/51210/3 "2001-01-22T05:30:26Z")

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Thank you very much, Cabbage 🙂

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**Author:** ![Enderw24](https://avatars.discourse-cdn.com/v4/letter/e/ba9def/32.png) [@Enderw24](https://boards.straightdope.com/u/Enderw24)\
**Post date:** [January 22, 2001, 5:50am UTC](https://boards.straightdope.com/t/regular-savings-geometric-progression-question/51210/4 "2001-01-22T05:50:34Z")

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The final number is based upon how long you’re keeping it in there and, just as important, how they calculate interest. 15% interest in one lump sum is a lot different than a daily interest that adds up to 15%.