Anybody good with maths? (ChatGPT failed me)

[Peri]

I'm trying to get a calculation solved - I've asked the all knowing Chatgpt this question and got 3 different answers !

So, If I start with an initial investment of £30,000 which grows at 7%, and I top that up with £500 every month (which I increase by 3% a year), how much would I have after 10 years?

GPT has told me £120,048.05 , £146,883.94 and £112,245.33

You can stop reading now - but just for completeness here are the questions and it's responses.

Starting with £30,000, and assuming a 7% return, and re-investing dividends, and adding in £500 every month which i increase by 3% per year, how much would there be after 10 years?

To calculate this, we can use the formula for future value of an annuity with increasing payments:

FV = P * ((1 + r)^n - 1) / r + PMT * ((1 + g) * ((1 + r)^n - 1) / (r - g))

Where:
FV = the future value of the investment
P = the principal amount invested (in this case, £30,000)
r = the annual interest rate (7% or 0.07, in this case)
n = the number of years the investment is held (10 years, in this case)
PMT = the monthly contribution (in this case, £500)
g = the rate of increase of the monthly contribution (3% or 0.03, in this case)

Plugging in the values, we get:

FV = £30,000 * ((1 + 0.07)^10 - 1) / 0.07 + £500 * ((1 + 0.03) * ((1 + 0.07)^10 - 1) / (0.07 - 0.03))

FV = £120,048.05

Therefore, assuming a 7% annual return, reinvesting dividends, and adding in £500 a month which increases by 3% per year, starting with an initial investment of £30,000, the investment would be worth approximately £120,048.05 after 10 years.

Starting with £30,000, and assuming a 7% return, and re-investing dividends, and adding in £500 every month which i increase by 3% per year, how much would there be after 10 years?

To calculate this, we can use the formula for future value of an annuity with increasing payments:

FV = PMT * ((1 + g) * ((1 + r)^n - 1) / (r - g)) + P * (1 + r)^n

Where:
FV = the future value of the investment
PMT = the monthly contribution (in this case, £500)
g = the rate of increase of the monthly contribution (3% or 0.03, in this case)
r = the annual interest rate (7% or 0.07, in this case)
n = the number of years the investment is held (10 years, in this case)
P = the principal amount invested (in this case, £30,000)

Plugging in the values, we get:

FV = £500 * ((1 + 0.03) * ((1 + 0.07)^10 - 1) / (0.07 - 0.03)) + £30,000 * (1 + 0.07)^10

FV = £146,883.94

Therefore, assuming a 7% annual return, reinvesting dividends, and adding in £500 a month which increases by 3% per year, starting with an initial investment of £30,000, the investment would be worth approximately £146,883.94 after 10 years.

starting with an initial investment of £30,000 which grows by 7% a year, and adding £500 a month which grows by 3% a year, how much would I have after 10 years?

To calculate this, we can use the formula for future value of an annuity:

FV = PMT * (((1 + r)^n - 1) / r) + P * (1 + r)^n

Where:
FV = the future value of the investment
PMT = the monthly contribution (in this case, £500)
r = the annual interest rate (7% or 0.07, in this case)
n = the number of years the investment is held (10 years, in this case)
P = the principal amount invested (in this case, £30,000)

We also need to take into account the increase in the monthly contribution by 3% per year, which we can calculate using the formula for future value of a single sum:

FV = P * (1 + r)^n

Where:
FV = the future value of the single sum
P = the principal amount invested (in this case, £500)
r = the annual interest rate (3% or 0.03, in this case)
n = the number of years the investment is held (10 years, in this case)

Plugging in the values, we get:

Monthly contribution at year 10 = £500 * (1 + 0.03)^10 = £670.56

FV = £500 * (((1 + 0.07)^10 - 1) / 0.07) + £30,000 * (1 + 0.07)^10 + £670.56 * ((1 + 0.07)^10 - 1) / 0.07

FV = £112,245.33

Therefore, assuming an initial investment of £30,000 that grows at a rate of 7% per year, and adding a monthly contribution of £500 that grows at a rate of 3% per year, the investment would be worth approximately £112,245.33 after 10 years.

 

[Phil]

I think it was Einstein who described the compounded interest calculation as the greatest ‘invention’ of all times.

I did a simple Excel sheet for 120 months

Capital = 30000
Interest PA 7%
Monthly Top Up 500
Increase Top Up 3%

Calculations:
Month 1 = (30000 x 7%)/12 = 175 = 30175 No Top Up in month 1
Month 2 = ((30175 + 500) x 7%)/12 = 179 = 31354
And so on …
In month 13 increase the 500 by 3% = 515
Increase in the other 13th month

Result:
Initial investment 30,000
Top Up 500 per month increased by 3% annually 68,283
Interest over 120 months 59,115
Total 157,398


Without the 3% increase the top up for 119 months is 59,500 and the interest 56,832
Total 146,332

Without the 500 top up the interest is 30,290
Total 60290

 

[Peri]

Thank you very much Phil.

This has now become an exercise in finding two answers that agree

I was told elsewhere that it was important to state to GPT when the interest was applied, so I refined my question, which gives yet another total. (I'm starting to see why financial advisers earn their money haha)

Starting with £30,000, and assuming a 7% annual return, and re-investing dividends, and adding in £500 every month which i increase by 3% per year every January 1st, how much would there be after 10 years?

Assuming a 7% annual return, reinvesting dividends, and adding in £500 a month which increases by 3% per year on January 1st, starting with an initial investment of £30,000, the investment would be worth approximately £133,868.94 after 10 years.

To calculate this, we can break the investment period down into smaller time intervals to account for the annual increase in the monthly contribution. Here's one way to do it:

For the first year, we can calculate the future value of the initial investment and the 12 monthly contributions of £500 each, with no increase:

FV1 = £30,000 * (1 + 0.07)^1 + £500 * [(1 + 0.07)^12 - 1] / 0.07
FV1 = £39,590.16

For the second year, we can calculate the future value of the investment as of January 1st, after one year of contributions, and then add the 12 monthly contributions of £515 each (the original £500 plus the 3% increase):

FV2 = (FV1 + £500) * (1 + 0.07)^1 + £515 * [(1 + 0.07)^12 - 1] / 0.07
FV2 = £51,023.09

For the third year and beyond, we can repeat the same process, taking the current value of the investment as of January 1st, adding the annual contribution, and then adding the 12 monthly contributions with the appropriate increase:

FV3 = (FV2 + £530) * (1 + 0.07)^1 + £531.45 * [(1 + 0.07)^12 - 1] / 0.07
FV3 = £64,598.61

FV4 = (FV3 + £546.90) * (1 + 0.07)^1 + £548.86 * [(1 + 0.07)^12 - 1] / 0.07
FV4 = £80,564.44

FV5 = (FV4 + £563.85) * (1 + 0.07)^1 + £566.37 * [(1 + 0.07)^12 - 1] / 0.07
FV5 = £99,204.80

FV6 = (FV5 + £581.32) * (1 + 0.07)^1 + £584.42 * [(1 + 0.07)^12 - 1] / 0.07
FV6 = £120,854.31

FV7 = (FV6 + £599.33) * (1 + 0.07)^1 + £603.02 * [(1 + 0.07)^12 - 1] / 0.07
FV7 = £145,907.11

FV8 = (FV7 + £617.88) * (1 + 0.07)^1 + £622.17 * [(1 + 0.07)^12 - 1] / 0.07
FV8 = £174,814.20

FV9 = (FV8 + £636.99) * (1 + 0.07)^1 + £641.89 * [(1 + 0.07)^12 - 1] / 0.07
FV9 = £208,098.01

FV10 = (FV9 + £656.67)

Not sure I completely understand its reply - FV9 = £208,098.01 ??


I just wish I'd taken more of an interest (!) in compound interest and the effect it could have on me personally 30 years ago.

 

[John Brown]

Not directly relevant, but an interesting rule of thumb is the rule of 72. If you take your compound interest rate, n, then your investment will double in 72/n years.
Not 100% accurate, but close enough for jazz.

 

[MartinF]

For anyone interested (probably unlikely), a good source of reference is “Compound Interest and Annuities Certain” by D W A Donald.

https://books.google.co.uk/books?id=zoG ... &q&f=false

I have a copy somewhere in the loft, unopened since 1971. What’s more, since then, I’ve forgotten most of the theory and would have to go back to using a spreadsheet as Phil has done.

However, with regard to the OP’s question, in order to be absolutely accurate , one needs to be more precise regarding the interest rate and date of payment of the monthly instalment. In the case of the monthly instalment, is it paid at the beginning, end or some intermediate point during the month. With regard to the interest rate, is the interest compounded monthly or annually i.e. is the interest rate 0.25% per month or (1.03^0.083333) per month to give 3% p.a.

 

[AndyP]

Wow.
My solution to calculating this sort of stuff was to marry an accountant. Makes my head hurt just reading this stuff.

 

[Phil]

Generally the banks calculate the interest at the end of the month, or do it on a daily balance which would be far more accurate, but would only credit the account at month end (first day of new month).

In my example I took the balance at end previous month, then added the 500 and then calculated the interest for that month. That would assume that the 500 is deposited on the 1st and the interest calculated at the end of that month.
Again it would not be a material difference.

Unless you are doing an actuarial calculation exercise, then my spreadsheet method would be accurate enough.

When I check my fixed deposit investment I use the spreadsheet-long-winded-way as well as the FV/PV calculations.
The difference is negligible over the 5 years term.

When doing the calculation it does not matter in which month it starts as it will be for 10 years or 120 months.

Another actual example:
Invest 70,000
Period 5 years
Interest 9% pa

Results of a Retail Bond fixed deposit:
Excel calculation value at end of 5 years 109,598
FV calculation 107,704
Actual pay out 108,745

Difference Excel to Actual 852 or 170 per year

Wow.
My solution to calculating this sort of stuff was to marry an accountant. Makes my head hurt just reading this stuff.

Andy ask your accountant to give us an example using the 10 year scenario

 

[Cabinetman]

More to the point, who's giving you 7%? !!

 

[Windows]

ChatGPT is not a software product that is designed to give correct answers. At best, it can produce plausible text. Correctness, when it arises, is best viewed as coincidental. Please don’t use ChatGPT for anything other than entertainment. It is the wrong tool for financial calculations.

 

[StevieB]

The difference is negligible over the 5 years term.

Difference Excel to Actual 852 or 170 per year

If the difference is negligible, I am happy to take your £852 off your hands every 5 years, and any other negligible amounts you may not want to bother with - I am sure I can find a use for such trivial sums of money

 

[Phil]

The difference is negligible over the 5 years term.

Difference Excel to Actual 852 or 170 per year

If the difference is negligible, I am happy to take your £852 off your hands every 5 years, and any other negligible amounts you may not want to bother with - I am sure I can find a use for such trivial sums of money

At current X-Rate it is GBP42.60 pa = maybe 20 pints :lol:

 

[Peri]

Thanks for all the time and effort folks

Windows - it's maths, I thought computers were good at maths !

 

[greeno]

ChatGPT is not a software product that is designed to give correct answers. At best, it can produce plausible text. Correctness, when it arises, is best viewed as coincidental. Please don’t use ChatGPT for anything other than entertainment. It is the wrong tool for financial calculations.

It's far more powerful than you make out, you might want to talk to the Samsung engineers who've been feeding it confidential information to optimise their test code.

 

[Windows]

ChatGPT’s lossy text compression is not a design that leads to correctness or reliability at the semantic level. It has some interesting properties, but people are getting confused by how it works and expecting it to do more than it can. It doesn’t do calculations, it doesn’t store facts, it’s not intelligent. Statistical relationships between words only gets you so far.

https://www.newyorker.com/tech/annals-of-technology/chatgpt-is-a-blurry-jpeg-of-the-web

https://www.newyorker.com/science/a...elligence/what-kind-of-mind-does-chatgpt-have

I saw a thread on Mastodon recently where university professors were complaining because their students were asking them for copies of papers that ChatGPT suggested that they had written, but that didn’t exist. The students expected ChatGPT to be giving them facts, but all ChatGPT has to offer is statistical relationships between words. ChatGPT doesn’t know which papers have been authored by any particular professor, but it can put together plausible sounding titles, because it locates words in a multidimensional space in a way that allows it to generate convincing sentences. If there are professors with unique names and unconventional titles to their papers, ChatGPT might be able to produce sentences that associate their names with their papers, but it’s a coincidence of the design, not a feature that can be relied upon.