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
So

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.

Cheers
Penny

Go to Math Central

To return to the previous page use your browser's back button.