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| − | Financial use of e | + | === Financial use of e === |
| − | + | Bernoulli discovered this constant in 1683 by studying a question about compound interest, but people in far more ancient time already came up with similar question. For example, a clay tablet from Mesopotamia, dated to about 1700 B.C. and now in the Louvre, poses the following problem: How long will it take for a sum of money to double if invested at 20 percent interest rate compounded annually? We now know this could be solved by using logarithms which the Babylonians did not have. | |
Suppose we have $100 (the "principal") in bank that pays 5% interest compounded annually. At the end of one year, our balance will be 100 x 1.05 = $105. At the end of the second year the balance will therefore be 105 x 1.05 = $110.25, at the end of the third year 110.25 x 1.05 = $115.76, and so on. | Suppose we have $100 (the "principal") in bank that pays 5% interest compounded annually. At the end of one year, our balance will be 100 x 1.05 = $105. At the end of the second year the balance will therefore be 105 x 1.05 = $110.25, at the end of the third year 110.25 x 1.05 = $115.76, and so on. | ||
It is easily to get the formula: | It is easily to get the formula: | ||
| Line 17: | Line 17: | ||
</gallery> | </gallery> | ||
As the n increases we have: | As the n increases we have: | ||
| − | + | {| class="wikitable" | |
| − | + | |- | |
| − | + | | n || (1+1/n)^n | |
| + | |||
| + | |- | ||
| + | | 5|| 2.48832 | ||
| + | |- | ||
| + | | 50 || 2.69159 | ||
| + | |- | ||
| + | | 100|| 2.70481 | ||
| + | |- | ||
| + | | 100,000|| 2.71827 | ||
| + | |- | ||
| + | | 1,000,000|| 2.71828 | ||
| + | |} | ||
Revision as of 14:46, 1 December 2018
Financial use of e
Bernoulli discovered this constant in 1683 by studying a question about compound interest, but people in far more ancient time already came up with similar question. For example, a clay tablet from Mesopotamia, dated to about 1700 B.C. and now in the Louvre, poses the following problem: How long will it take for a sum of money to double if invested at 20 percent interest rate compounded annually? We now know this could be solved by using logarithms which the Babylonians did not have. Suppose we have $100 (the "principal") in bank that pays 5% interest compounded annually. At the end of one year, our balance will be 100 x 1.05 = $105. At the end of the second year the balance will therefore be 105 x 1.05 = $110.25, at the end of the third year 110.25 x 1.05 = $115.76, and so on.
It is easily to get the formula:
Cumulated money(S) Principal (P) Interest rate(r) Time(t)
This formula is the basis of financial math,and it will apply to bank accounts, loans, mortgages, or annuities.
Since time could be other than year more precise formula would be;
Let the annual interest rate be 100% then we have
As the n increases we have:
| n | (1+1/n)^n |
| 5 | 2.48832 |
| 50 | 2.69159 |
| 100 | 2.70481 |
| 100,000 | 2.71827 |
| 1,000,000 | 2.71828 |
