Mathematician wanted

Brunokid

Mr Bags has £1,000,000 in savings earning 3% net interest every year.
At the end of every year he withdraws £60,000 in total to purchase the following years supply of chocolate.
He obviously needs to draw down from his capital every year but how long until he has nothing left? (cash that is, not chocolate)

Thanks in advance 
Bruno

DullGreyGuy

At the end of year 23 they cannot afford their chocolate purchase

bsms1147

I made it end of year 24

eddddy

If I've understood the question correctly, at the end of year 23, they'll have £26,413.49 left. So not enough to buy £60k worth of chocolate.

MX5huggy

Inflation will make the chocolate more expensive. Mr Bags will have to have less and less chocolate each year or have chocolate for fewer years. Maybe he should invest in a chocolate factory to attempt to keep up with inflation. 

maman

Surely this is Mr Creosote not Mr Bags? 🤔

jak22

It's interesting to see how AI handled this question

The first response (with an explanation of the working) concluded that

We can see that his capital decreases each year. To find out when he will have nothing left, we need to calculate year by year until the capital is exhausted.

After around 25 years, he will have less than £60,000 left, and after the 26th year, his capital will be depleted.

Therefore, Mr. Bags will run out of his savings in about 26 years.

Asked to refine, the response was a Python prog which also concluded 

In this calculation, Mr. Bags' savings will last for approximately 26 years. After the 26th year, he will have depleted his capital.

Prompted with asking how long until he cant afford to buy a supply of chocolate, the response was more Python and

Based on this calculation, Mr. Bags will be able to afford his annual chocolate supply for approximately 21 years. After the 21st year, his capital plus interest will no longer be enough to cover the £60,000 withdrawal.

SnowMan

Mr Bags will be diagnosed with type 2 diabetes after 1 year 61 days.

At that point he will either have to stop buying the chocolate, or will die from a diabetes related complication before the money runs out to buy the chocolate.

OldScientist

If you want to calculate this sort of thing yourself, the nper function in your favourite(!) spreadsheet program will do it.

nper(3%,60000,-1000000,0,0)=23.44

where 3% is the interest rate, 60000 is the withdrawal, -1000000 the starting amount, 0 the final amount, and the final 0 indicates withdrawals at the end of each year.

You get 23 years of the full £60k amount.

boingy

I'm not sure he should be spending his entire pension pot on chocolate.

PeskyBlunder

Did Mr Bags win bigly on the PBs?