incremental savings: Over X months I want to save Y dollars.... I want to increase the monthly contribution at a rate of Z %.

[sveard]

Hi everyone. I'm new here.
Math (and school in general) was a looong time ago and I don't know how to do the following:

Over X months I want to save Y dollars.
For example, in 10 months I want to save 1000 dollars.
This is a monthly contribution to savings of 100 dollars.

But I do not want to contribute a fixed amount each month.
I want to increase the monthly contribution at a rate of Z %.
Let's say I start with 100 dollars and increase this at a rate of 2%.

First month	100
Second month	102
3	104,04 (2% of 102)
4	106,12 (2% of 104,04)
5	108,24
6	110,41
7	112,62
8	114,87
9	117,17
10	119,51

This adds up to a total of 1094,97 which is too much.

Am I wrong in thinking it's impossible to calculate the starting contribution if only the desired total savings Y, the period X and the monthly contribution increase Z% are known?

I'm not looking for a formula (but wouldn't mind getting one of course) but it would be super helpful if someone could point me in the right direction. I would be thankful either way

 

[stapel]

Hi everyone. I'm new here.
Math (and school in general) was a looong time ago and I don't know how to do the following:

Over X months I want to save Y dollars.
For example, in 10 months I want to save 1000 dollars.
This is a monthly contribution to savings of 100 dollars.

But I do not want to contribute a fixed amount each month.
I want to increase the monthly contribution at a rate of Z %.
Let's say I start with 100 dollars and increase this at a rate of 2%.

First month	100
Second month	102
3	104,04 (2% of 102)
4	106,12 (2% of 104,04)
5	108,24
6	110,41
7	112,62
8	114,87
9	117,17
10	119,51

This adds up to a total of 1094,97 which is too much.

Am I wrong in thinking it's impossible to calculate the starting contribution if only the desired total savings Y, the period X and the monthly contribution increase Z% are known?

I'm not looking for a formula (but wouldn't mind getting one of course) but it would be super helpful if someone could point me in the right direction. I would be thankful either way

To find a pattern, don't simplify.

After zero compoundings, you have 100.

After one compounding, you have 100*(1.02).

After two compoundings, you have (100*(1.02))*(1.02) = 100*(1.02)^2.

After three compoundings, you have (100*(1.02)^2))*(1.02) = ...

And so forth. What pattern do you find for the n-th compounding?

 

[Dr.Peterson]

Over X months I want to save Y dollars.
For example, in 10 months I want to save 1000 dollars.
This is a monthly contribution to savings of 100 dollars.

But I do not want to contribute a fixed amount each month.
I want to increase the monthly contribution at a rate of Z %.
Let's say I start with 100 dollars and increase this at a rate of 2%.

First month	100
Second month	102
3	104,04 (2% of 102)
4	106,12 (2% of 104,04)
5	108,24
6	110,41
7	112,62
8	114,87
9	117,17
10	119,51

This adds up to a total of 1094,97 which is too much.

Am I wrong in thinking it's impossible to calculate the starting contribution if only the desired total savings Y, the period X and the monthly contribution increase Z% are known?

I'm not looking for a formula (but wouldn't mind getting one of course) but it would be super helpful if someone could point me in the right direction. I would be thankful either way

You've been given a hint: If you look up compound interest, you can find some formulas that could be helpful if you change the percent increase.

But what you want is simpler than that!

You've found that if the first payment is $100, the total over 10 months is $1094.97. How would the total change if you doubled the starting amount?

Now, could you multiply the starting amount by something else to get the desired total of $1000?

What you want to calculate is entirely possible, and in fact entirely within your current abilities.

 

[khansaheb]

Hi everyone. I'm new here.
Math (and school in general) was a looong time ago and I don't know how to do the following:

Over X months I want to save Y dollars.
For example, in 10 months I want to save 1000 dollars.
This is a monthly contribution to savings of 100 dollars.

But I do not want to contribute a fixed amount each month.
I want to increase the monthly contribution at a rate of Z %.
Let's say I start with 100 dollars and increase this at a rate of 2%.

First month	100
Second month	102
3	104,04 (2% of 102)
4	106,12 (2% of 104,04)
5	108,24
6	110,41
7	112,62
8	114,87
9	117,17
10	119,51

This adds up to a total of 1094,97 which is too much.

Am I wrong in thinking it's impossible to calculate the starting contribution if only the desired total savings Y, the period X and the monthly contribution increase Z% are known?

I'm not looking for a formula (but wouldn't mind getting one of course) but it would be super helpful if someone could point me in the right direction. I would be thankful either way

Your calculations indicate that the interest rate is:

2% per month.​

Interest rates are generally reported PER YEAR (per year or per annum).
Please confirm the time period for the reported interest rate.

 

[sveard]

You've found that if the first payment is $100, the total over 10 months is $1094.97. How would the total change if you doubled the starting amount?

Okay this I think helped me.
Doubling the starting amount (100 -> 200) means doubling the total over 10 months (1094,97 -> 2189,94).

Now, could you multiply the starting amount by something else to get the desired total of $1000?

I think: 100 * 1000 / 1094,97 = 100 * 0,9133 = 91,33.

First month	91,33
Second month	93,15
3	95,02
4	96,92
5	98,85
6	100,83
7	102,85
8	104,91
9	107,00
10	109,14

I believe that this is what you wanted me to find out?

2% per month. Interest rates are generally reported PER YEAR (per year).
Please confirm the time period for the reported interest rate.

Yes, I need this monthly.

 

[Dr.Peterson]

Your calculations indicate that the interest rate is:

2% per month.​

Interest rates are generally reported PER YEAR (per year or per annum).
Please confirm the time period for the reported interest rate.

I don't think the question is about compound interest, but about a consistent percent increase each month, so norms for interest on loans would not be relevant. I only mentioned compound interest because it follows the same formula. Also, the ultimate question is about the sum of these increasing amounts, which will similarly parallel annuity calculation, though the problem is very different.

The subject could also be approached in terms of geometric series.

But I do not want to contribute a fixed amount each month.
I want to increase the monthly contribution at a rate of Z %.
Let's say I start with 100 dollars and increase this at a rate of 2%.

 

[sveard]

I don't think the question is about compound interest, but about a consistent percent increase each month, so norms for interest on loans would not be relevant. I only mentioned compound interest because it follows the same formula. Also, the ultimate question is about the sum of these increasing amounts, which will similarly parallel annuity calculation, though the problem is very different.

This is exactly what I meant but was unable to convey clearly (English is not my native language and I'm not very fluent in mathematics/finance).

 

[The Highlander]

This is exactly what I meant but was unable to convey clearly (English is not my native language and I'm not very fluent in mathematics/finance).

An Excel™ spreadsheet might also be a useful tool in your 'endeavours'.

Do you know how to "copy down" cells in one?

You could set up Z as an initial variable, enter a "starting contribution" (M₁) and, with the right formula* and running totals, see what you would get after any (desired?) number of months.
Once that's "up & running" varying Z and M₁ would allow you to explore the 'outcomes' until you got one you liked.

If that's of interest but you simply haven't got any clue how to set it up, let me know; I may be able to create one for you over the weekend (if I get any spare time).


* You could use: M_(n+1) = M_n × (1+Z)

Where the M_n are your (calculated) monthly contributions (M₁ being your "starting contribution") and Z is your monthly interest rate (converted from a percentage fraction to a decimal fraction)

 

[The Highlander]

@sveard

Hi,

I did manage to put together a small Excel™ spreadsheet over the weekend (turned out it was just a ten minute job ?).

Using the spreadsheet it’s a simple matter to vary the “starting contribution” and the ‘percentage increase in contributions’ to get any desired total “saved” over a particular period of time.

Below are pics of two “analyses” I ran through the spreadsheet.

The first just uses your own suggested parameters and shows that it can quickly determine that you should start off by contributing $91.33 if you want to increase your monthly contributions by 2% each month and end up with (approximately, within a few cents) $1,000 after ten months.

The second shows that you need to increase your monthly contributions by 2.32% each month if you want to start off by putting in, say, $90 and still end up with $1,000 (plus 2¢ ) at the end of the same period.

If you want a copy of the spreadsheet just let me know. ?

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