WORLD OF FIGURES: Even with inflation you can’t finish Sh240m ever!

Saturday November 4 2017

The answer was shocking: at that withdrawal

The answer was shocking: at that withdrawal rate, money would never get finished – never ever. PHOTO| FILE| NATION MEDIA GROUP 

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Last week we attempted to answer this question: if you have Sh240 million in a bank account and you spent Sh10,000 daily, how long would the money last? The answer was shocking: at that withdrawal rate, money would never get finished – never ever. It would last until the end of the world!

The reason is that, each day, the Sh240 million earns more than Sh10,000 in interest. Therefore, as we found out, your balance would gradually increase even though you are removing a large sum daily.

But then a second question popped up: what if you wanted to maintain the same lifestyle that costs Sh10,000 today? That is, buy the same quality and quantity of goods for as long as possible: how long would the Sh240 million last?

To get the answer, we need to account for inflation. Records from the Kenya National Bureau of Statistics indicate that the consumer price index in Kenya increased from 0.93 in 1961, when data collection started, to 185.39 in June this year.

This means that over the past 56 years, the general prices of goods and services in Kenya have increased by a factor of 199.34 – almost 200 times. In other words, an item that cost one shilling in 1961 will most likely cost about Sh200 today. From this data, it turns out that the average annual inflation rate over the last 56 years was about 9.92 per cent. It is reasonable to use this long-term average rate to project to the future. Indeed, in order to simplify the calculation, we may round it off to 10 per cent.

Thus, in the first year you would deduct Sh10,000 daily (Sh3.65m in total); then increase that to Sh11,000 in the second year (Sh4.015m in all); then to Sh12,100 in the third (Sh4.4m) and so on.

At the same time, the bank will pay you interest on the balance in your account; perhaps a modest rate of 7 per cent per annum. Your principal balance in the first year will vary from Sh240m in the beginning to Sh236.35m at the end.

Thus the average balance during the year will be Sh238.175m. Therefore, at the rate of 7 percent per annum, you will earn an interest of about Sh16.67m. Consequently, at the end of the first year, you will have withdrawn Sh3.65m and the bank will pay Sh16.67m; the net result is an addition of about Sh13m. In other words, you balance will have increased from Sh240m to Sh253m.

Again we find that, even if we accounted for inflation, you would still be taking out less money than what the bank is paying you. So you still cannot finish the Sh240m – never, ever!

This is the sort of thing that happens to the Nobel Prize Fund. Every year since 1901, they pay out large sums of money to the winners but the kitty is never depleted.