Math 1 · Unit 8 · Lesson 4 · part 2 of 5
Kevin and Joseph: $5 a month, or 3% a month?
Two friends each invest $100.
Kevin and Joseph: $5 a month, or 3% a month?
Two friends each invest $100. They get paid in different ways.
Kevin: $5 every month
The same dollars added each month: a constant difference. Lines add.
K(m) = 100 + 5m
This is simple interest: $5 is 5% of the original $100, paid every month on the principal only.
Joseph: 3% every month
The same percent each month: multiply by 1 + 0.03 = 1.03, a constant ratio. Exponentials multiply.
J(m) = 100(1.03)m
This is compound interest: each month's 3% is on everything in the account.
Who would you rather be? Kevin's 5% sounds better than Joseph's 3%, and for a long time it is.
| month | Kevin: 100 + 5m | Joseph: 100(1.03)m | ahead |
|---|---|---|---|
| 0 | $100.00 | $100.00 | tie |
| 6 | $130.00 | $119.41 | Kevin |
| 12 | $160.00 | $142.58 | Kevin |
| 24 | $220.00 | $203.28 | Kevin |
| 30 | $250.00 | $242.73 | Kevin |
| 32 | $260.00 | $257.51 | Kevin |
| 33 | $265.00 | $265.23 | Joseph |
| 36 | $280.00 | $289.83 | Joseph |
| 48 | $340.00 | $413.23 | Joseph |
After two years (24 months) Kevin is well ahead, $220.00 to $203.28. That surprises people. But look at months 32 and 33: Joseph catches up and passes him, and by month 48 Joseph is ahead by more than $70. Run the race yourself.