How does one go about proving that the limit of i^p as p approaches infinity is equal to the force of interest?

Login

0 votes

Best answer

To prove that the limit as p appraoches infinity of i^(p) you can use Eulers rule.

Recall that the $$\lim\limits_{n \rightarrow \infty} (1 + \frac{x}{n})^n = e^x $$

By definition you also know that $$(1+i) = (1+\frac{i^(p)}{p})^p$$

therefore $$\lim\limits_{n \rightarrow \infty} (1 + \frac{i^(p)}{p})^p = e^{i(\infty)}$$

and so $$ i^{\infty} = \delta$$

- All categories
- BUS 1003H - Introduction to Financial Risk (52)
- BUS 2016H - Financial Mathematics (55)
- BUS 3018F - Models (74)
- BUS 3024S - Contingencies (61)
- BUS 4028F - Financial Economics (39)
- BUS 4027W - Actuarial Risk Management (56)
- BUS 4029H - Research Project (5)
- Mphil (1)
- Calculus and Pure Mathematics (4)
- Statistics (16)

...