3.1 If you open a savings account that earns 7.5% simple interest per year, what is the minimum num- ber of years you must wait to double your balance? Suppose you open another account that earns 7% interest compounded yearly. How many years will it take now to double your balance?
| 7.5% Simple Interest | 7% Compound Interest | |||||||||
| Assume we start with $1 | ||||||||||
| Year | Opening Balance | Interest @ 7.5 % | Closing Balance | Opening Balance | Interest @ 7 % | Closing Balance | ||||
| 1 | 100.00 | 7.50 | 107.50 | 100.00 | 7.00 | 107.00 | ||||
| 2 | 107.50 | 7.50 | 115.00 | 107.00 | 7.49 | 114.49 | ||||
| 3 | 115.00 | 7.50 | 122.50 | 114.49 | 8.01 | 122.50 | ||||
| 4 | 122.50 | 7.50 | 130.00 | 122.50 | 8.58 | 131.08 | ||||
| 5 | 130.00 | 7.50 | 137.50 | 131.08 | 9.18 | 140.26 | ||||
| 6 | 137.50 | 7.50 | 145.00 | 140.26 | 9.82 | 150.07 | ||||
| 7 | 145.00 | 7.50 | 152.50 | 150.07 | 10.51 | 160.58 | ||||
| 8 | 152.50 | 7.50 | 160.00 | 160.58 | 11.24 | 171.82 | ||||
| 9 | 160.00 | 7.50 | 167.50 | 171.82 | 12.03 | 183.85 | ||||
| 10 | 167.50 | 7.50 | 175.00 | 183.85 | 12.87 | 196.72 | ||||
| 11 | 175.00 | 7.50 | 182.50 | 196.72 | 13.77 | 210.49 | ||||
| 12 | 182.50 | 7.50 | 190.00 | |||||||
| 13 | 190.00 | 7.50 | 197.50 | |||||||
| 14 | 197.50 | 7.50 | 205.00 | |||||||
| Minimum Number of years needed to double balance = 14 Years | Minimum Number of years needed to double balance = 11 Years | |||||||||
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