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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)?

Amaan M
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Toby Cannon
  • 139
  • Do you know the formula for compound interest? – Amaan M May 05 '21 at 18:32
  • Sorry, I appreciate I wasn't too clear. It's compound interest, but I'm struggling to work out the total. So not the amount I have on week 30, but how much I have if I added up day 1 + day 2 + day 3 etc. Does this make more sense? – Toby Cannon May 05 '21 at 18:47
  • Yes, that makes more sense. Think about what happens in that total column. What's 20.5? It's actually $10+101.05$, then that $31.525$ is actually $10+101.05+101.05^2$. So, if you sum up that total column all the way, you'll end up with $10$ being included in all 30 rows, $101.05$ 29 times, $101.05^2$ 28 times, etc. So, you overall total is $1030+101.0529+101.05^228+...+10*1.05^{29}$. Set that equal to $1500$, replace the $10$ with a variable (since that was meant to be your principal), and you've got your formula. – Amaan M May 05 '21 at 19:12

1 Answers1

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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

Henry
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  • Sorry, I appreciate I wasn't too clear. It's compound interest, but I'm struggling to work out the total. So not the amount I have on week 30, but how much I have if I added up day 1 + day 2 + day 3 etc. Does this make more sense? – Toby Cannon May 05 '21 at 18:55
  • @TobyCannon Not really: the point about compound interest is that you multiply at each stage rather than add – Henry May 05 '21 at 19:01
  • So it would compound at each stage. I'm trying to find out what the initial value would be if I want to add up all values in the series and the final total value to be 1500 – Toby Cannon May 05 '21 at 19:08
  • @TobyCannon That suggests you are adding an extra amount $x$ each time. Does the initial amount get $30$ doses of compound interest and the last $x$ only $1$ dose? If so, you get $1.05^{30}x + 1.05^{29}x + \cdots + 1.05^{1}x = 1500$ and you need to use the geometric series. – Henry May 05 '21 at 19:13