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Write-up


Title
I want to be a millionaire!


Problem Statement
If I put $1.00 in the bank, how many years would it take for me to become a millionaire if my money doubled each year?

Problem setup

This problem involves using the power of exponents.

 

Plans to Solve/Investigate the Problem

We guessed some different possibilities for this. We then decided to put numbers into an Excel spreadsheet with 3 columns labeled Year, $ and Powers.

 

Investigation/Exploration of the Problem

The first number in the "Year" column is 1 for the first year and for every year thereafter, the A rows are labeled up to 21. The first number in the "$" column is 1 for the one dollar I put in the bank the first year. The first power in the "Powers" column is 1 because in the first year my $1.00 is just one dollar or one to the first power. We put the following formula in cell B3: =B2*2. We used the black plus cursor to drag the column down so that Excel could calculate the money for each year. We put the following formula in cell C2: =2^(A2-1). The same procedure for using the black plus and dragging down is used for this formula for Excel to calculate the values. The numbers in the "$" column  and the "Powers" column should be the same. The spreadsheet is as follows:

 

Year $ Powers
1 1 1
2 2 2
3 4 4
4 8 8
5 16 16
6 32 32
7 64 64
8 128 128
9 256 256
10 512 512
11 1024 1024
12 2048 2048
13 4096 4096
14 8192 8192
15 16384 16384
16 32768 32768
17 65536 65536
18 131072 131072
19 262144 262144
20 524288 524288
21 1048576 1048576

 

 

Extensions of the Problem

An extension of this problem was the following: If I want to be a millionaire in ten years, how much will my initial deposit in the bank have to be if my money doubled each year? We guessed various numbers and plugged them into Excel using the same formulas. The amount of money needed initially is $1954.00.

Author & Contact
Pam Joseph
mailto:prj1@aol.com

Link(s) to resources, references, lesson plans, and/or other materials
Link 1
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