Date: Sun, 08 Nov 1998 21:16:15 -0700
Subject: Depositing money. . .

It has been years since I was in school and I can't remember if there is a formula for the following problem:

If you deposit $1.00 on the first day of the month, $2.00 on the second day, $3.00 on the third day . . $31.00 on the last day of the month, how much do you have in the bank?

Now will this formula also work if it was, $0.25 (then day two you would deposit 2x $0.25 or $0.50, day three you would deposit 3x $0.25, $0.75. . . ). Will it work with any denomination??

Thank you for your time. I promise I'll write this one down for future reference. . .

Hi Gerry

The way the problem is stated you are not collecting any interest on your money. Thus what you want is the sum

S = 1 + 2 + 3 + ... + 31.

I won't tell you a formula as it's too easy to forget but I will show you how to do the sum.

Write the sum twice, the second time in reverse order.

S=1+2+ 3+...293031
S=31+30+ 29+...321
Now add down

2S=32+32+ 32+...323232

2S = 31(32)
and thus

Your second problem is handled in the same way, write the sum twice, the second time in reverse order and then add down.


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