Summer Tuggle
Assignment
12
Using Spreadsheets to Explore
Compound Interest
Pam
and Sam just graduated college and started their professional career. Pam is very cautious with her money and
decides to save $1000 a year. Sam is so
excited to finally have money that he spends all that he makes and saves
nothing. This continues for 10
years. At this point, Pam decides to let
loose and quits saving. She does not
make any withdrawals from her savings account; the money just sits there. Sam decides that he better get on the savings
train so he starts with $1000 a year.
Both accounts earn a fixed 6% interest rate.
Explore
this situation with a spreadsheet and graph.
Will Sam ever catch up to Pam’s savings?
If so, when will that happen?
|
year |
Pam |
Sam |
||
|
0 |
$1,000.00 |
$0.00 |
||
|
1 |
$1,060.00 |
$0.00 |
||
|
2 |
$2,183.60 |
$0.00 |
||
|
3 |
$3,374.62 |
$0.00 |
||
|
4 |
$4,637.09 |
$0.00 |
||
|
5 |
$5,975.32 |
$0.00 |
||
|
6 |
$7,393.84 |
Year 10 is
final contribution year for Pam.
Year 11 is the first year that Sam saves. |
||
|
7 |
$8,897.47 |
$0.00 |
||
|
8 |
$10,491.32 |
$0.00 |
||
|
9 |
$12,180.79 |
$0.00 |
||
|
10 |
$13,971.64 |
$0.00 |
||
|
11 |
$14,809.94 |
$1,060.00 |
||
|
12 |
$15,698.54 |
$2,183.60 |
||
|
13 |
$16,640.45 |
$3,374.62 |
||
|
14 |
$17,638.88 |
$4,637.09 |
||
|
15 |
$18,697.21 |
$5,975.32 |
||
|
16 |
$19,819.04 |
$7,393.84 |
||
|
17 |
$21,008.18 |
$8,897.47 |
||
|
18 |
$22,268.68 |
$10,491.32 |
||
|
19 |
$23,604.80 |
$12,180.79 |
||
|
20 |
$25,021.08 |
$13,971.64 |
||
|
21 |
$26,522.35 |
$15,869.94 |
||
|
22 |
$28,113.69 |
$17,882.14 |
||
|
23 |
$29,800.51 |
$20,015.07 |
||
|
24 |
$31,588.54 |
$22,275.97 |
||
|
25 |
$33,483.85 |
$24,672.53 |
||
|
26 |
$35,492.89 |
$27,212.88 |
||
|
27 |
$37,622.46 |
$29,905.65 |
||
|
28 |
$39,879.81 |
$32,759.99 |
||
|
29 |
$42,272.60 |
$35,785.59 |
||
|
30 |
$44,808.95 |
$38,992.73 |
||
|
31 |
$47,497.49 |
$42,392.29 |
||
|
32 |
$50,347.34 |
$45,995.83 |
||
|
33 |
$53,368.18 |
$49,815.58 |
||
|
34 |
$56,570.27 |
$53,864.51 |
||
|
35 |
$59,964.48 |
$58,156.38 |
||
|
36 |
$63,562.35 |
$62,705.77 |
||
|
37 |
$67,376.09 |
$67,528.11 |
||
|
38 |
$71,418.66 |
$72,639.80 |
||
|
39 |
$75,703.78 |
$78,058.19 |
||
|
40 |
$80,246.01 |
$83,801.68 |
||
|
41 |
$85,060.77 |
$89,889.78 |
||
|
42 |
$90,164.41 |
$96,343.16 |
||
|
43 |
$95,574.28 |
$103,183.75 |
||
|
44 |
$101,308.73 |
$110,434.78 |
||
|
45 |
$107,387.26 |
$118,120.87 |
The chart and the
graph show that Sam will catch up and surpass Pam at year 37 of saving. The blue curve shows that Pam’s savings rate
starts at a nice pace and then changes at year 10 (she quits contributing
$1000). It becomes a gentler curve. Sam’s savings don’t take off until year 10
and then it curves exponentially according to the growth factor of 1.06.
It is interesting
to note that if Pam had continued with saving $1000 a month for the 45 years,
she would have a total of $225,508.12.
See the graph below.
