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.

 

[John Brown]

A spreadsheet would do this easily, I think.

 

[Peri]

I'd assume it would be a fairly standard (and easy) query for someone with a financial background

 

[paulrbarnard]

It depends on when you calculate the percentages. For example is the three percent increase applied at a fixed time each year or is it incremented through the year to equate to 3%. This applies to all the factors and has a significant impact on the net amount

 

[Peri]

Right, that makes a lot of sense. I need to state that the £500 is increased by 3% once a year on a fixed date - which gives another answer.

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 every January 1st, you would have approximately £107,678.21 after 10 years.

 

[Bristol_Rob]

And what does 7 grand buy you these days

 

[Jones]

As above with compound interest ( interest on the interest) it makes a difference when the interest is calculated and applied , daily/ monthly/ annually etc

 

[paulrbarnard]

Right, that makes a lot of sense. I need to state that the £500 is increased by 3% once a year on a fixed date - which gives another answer.

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 every January 1st, you would have approximately £107,678.21 after 10 years.

This is one of the challenges with things like ChatGPT. While your original question looked unambiguous it could be interpreted in different ways. A human is still more able to decide ‘what was actually meant” and even ask clarifying questions. AI will get there soon but at its current evolution still conforms to the computing adage “garbage in garbage out”. This unfortunately applies to both the requests and the training material.

 

[Peri]

If you look at the first 3 questions I asked it, the first 2 were identical but received different answers - there's probably some insight into it's inner workings for someone more intelligent than me !

Refining the question further

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.

 

[akirk]

it is worth remembering that chatGPT and any other form of AI has no actual intelligence
so chatGPT works on algorithms and lots of data - if there is conflicting data purporting to answer the same question - how can it know which to use?
So if I put up a website with your question on and the answer of £4.50 - that information will feed into the algorithm... now I would guess that they have some sanity checking in the algorithms but feed it enough spurious data and it will start to consider it valid...

i.e. - don't rely on it for anything

 

[Spectric]

To get sensable output from a system you need to input all the data and be very specific with the question.

Yes AI is like a smart phone, one has no inteligence and the other is not smart.

If Chapgpt was inteligent then it would know that you have not provided sufficient data and not try and solve a partial question with spurious results and instead ask for you to provide the missing data.

This AI is an interesting subject, what makes it any different from combinational or sequential logic because all our computer technology is based on binary and simple logic like equal to or greater than so where does it's ability to be inteligent and make decisions not based on any pre programed algorithms come from, what is different or changed from say Von-Neumann architecture or Harvard architecture which we were taught at college.

 

[Stanleymonkey]

I did have a spreadsheet a long time ago for tracking my first mortgage. It's fairly straightforward to do..


I just googled compound interest for spreadsheets - this came up. A bit more advanced than what I used to do

Spreadsheet formula for compound interest

A more efficient way of calculating compound interest in Excel is applying the general interest formula: FV = PV(1+r)n, where FV is future value, PV is present value, r is the interest rate per period, and n is the number of compounding periods.

There are also lots of help and guidance sites. This was the first site listed:

https://www.excel-easy.com/examples/compound-interest.html

 

[Fitzroy]

Quick spreadsheet I get 147,716 with yearly interest 145,024 with monthly. Spreassheet in the zip file

 

[ChaiLatte]

The question is unanswerable as written (in post #9). As stated above, you need to specify how the interest is calculated. There is no small print to your question, and in this case it is very necessary.

On day 1, you have a balance of 30k. After one month, you deposit 0.5k. On that day, what is your balance?

The small print might say that interest is calculated daily but anything deposited into your account will only be subject to interest the next calender day to the deposit day.

How many days are possible in 'ten years'? 3652 or 3653 are possible.

Yearly interested calculated monthly is easy - divide by 12 - 120 periods over ten years. The difficulty with monthly interest is your question is indeterminate on how it interacts with the monthly balance top ups.

In a similar way, the question is indeterminate on how annual interest would interact with the monthly top ups - the 0.5k put in on Jan 1 might only be seen for interest purposes as part of 6k on Dec 31.

 

[Peri]

Thank you very much for some brilliant and helpful replies

Every day is a school day - I love learning !

Spreadsheet is great Fitz, thanks - and tallies up almost exactly with another answer I was given.

 

[ChaiLatte]

Quick spreadsheet...

So quick it neglects the annual 3% increase in monthly deposit. I won't invest with you. That is £180 of my money you have lost in just the first year, let alone not paying me interest on it.

If we cannot even calculate correctly the total amount deposited, what hope is there of a correct amount after interest?

In your sheet, he puts in his last monthly top up at end month 120 and receives 7% annual interest on it that same day. £35 interest in one day. I will be sure to invest with you.

Another thing to be specified by the OP is the total number of monthly deposits: 119 or 120.

Another another thing: the 3% uplift occurs on Jan 1. What if he opens the account on Dec 31? That means the very first monthly top up will be 515 rather than 500.

 

[Fitzroy]

So quick it neglects the annual 3% increase in monthly deposit. I won't invest with you. That is £180 of my money you have lost in just the first year, let alone not paying me interest on it.

If we cannot even calculate correctly the total amount deposited, what hope is there of a correct amount after interest?

In your sheet, he puts in his last monthly top up at end month 120 and receives 7% annual interest on it that same day. £35 interest in one day. I will be sure to invest with you.

Another thing to be specified by the OP is the total number of monthly deposits: 119 or 120.

Another another thing: the 3% uplift occurs on Jan 1. What if he opens the account on Dec 31? That means the very first monthly top up will be 515 rather than 500.

Feel free to correct it, update and repost.