Math 1 · Unit 8 · Lesson 4 · part 3 of 5
Two banks, two forms: City Bank and National Bank
Real choices come in different forms: one bank gives you a sentence, another a formula, another a table.
Two banks, two forms: City Bank and National Bank
Real choices come in different forms: one bank gives you a sentence, another a formula, another a table. Compare them by putting both in the same form. Two banks, $10,000 each.
City Bank: 3% simple interest
Adds 10,000 × 0.03 = $300 every year.
C(y) = 10,000 + 300y
A line: constant difference of $300.
National Bank: 2.6% compounded monthly
Rate per period 0.02612, and 12y periods (Lesson 3).
N(y) = 10,000(1 + 0.02612)12y
An exponential: constant ratio.
| year | City Bank | National Bank | ahead |
|---|---|---|---|
| 0 | $10,000.00 | $10,000.00 | tie |
| 5 | $11,500.00 | $11,386.68 | City Bank |
| 10 | $13,000.00 | $12,965.65 | City Bank |
| 11 | $13,300.00 | $13,306.81 | National Bank |
| 15 | $14,500.00 | $14,763.58 | National Bank |
| 20 | $16,000.00 | $16,810.82 | National Bank |
City Bank has the higher rate, 3% against 2.6%, and after 10 years it is still ahead, $13,000.00 to about $12,966. But National Bank takes the lead in year 11, and after 15 years it wins, about $14,764 to $14,500.00. After 20 years the gap is more than $800.