From Actuarial Outpost Wiki
These are my notes, and I hope you can find them useful
Contents |
Exam FM
Vivamus volutpat. Duis congue ullamcorper leo. Donec varius. In hac habitasse platea dictumst. Pellentesque nunc. Quisque malesuada sapien et justo. Quisque est orci, vulputate at, lacinia vel, pellentesque non, arcu. Proin et ante. Sed eget ante nec dui aliquet ultricies. Vivamus imperdiet, mauris a pretium viverra, dui arcu pulvinar urna, ut aliquam lectus dui nec ante.
Donec id orci et est porta elementum. Nunc at massa in mi sollicitudin ultrices. Integer erat. Sed vel tortor at tortor placerat mollis. Donec risus mauris, lobortis nec, ornare non, eleifend quis, erat. In tristique lorem quis felis. Phasellus ullamcorper lacus nec ligula. Phasellus semper ante et lorem. Mauris diam elit, dictum quis, pellentesque sed, varius eget, sem. Maecenas nec lacus nec felis vulputate consequat. Mauris arcu tortor, feugiat ac, suscipit auctor, vulputate eu, tortor. Pellentesque habitant morbi tristique senectus et netus et malesuada fames ac turpis egestas. Phasellus sit amet orci eget dui pellentesque ultrices. Vestibulum nibh leo, suscipit a, dignissim vitae, laoreet vel, lorem.
Formula List
Annuities: <math>a_{\overline{n|}}=\frac{1-v^n}{i}=v+v^2+..+v^n</math> : PV of an annuity-immediate.
<math>\ddot{a}_{\overline{n|}}=\frac{1-v^n}{d}=1+v+v^2+..+v^{n-1}</math> : PV of an annuity-due.
<math>\ddot{a}_{\overline{n|}}=(1+i)a_{\overline{n|}}=1+a_{\overline{n-1|}}</math>
<math>s_{\overline{n|}}=\frac{(1+i)^n-1}{i}=(1+i)^{n-1}+(1+i)^{n-2}+..+1</math> : AV of an annuity-immediate (on the date of the last deposit).
<math>\ddot{s}_{\overline{n|}}=\frac{(1+i)^n-1}{d}=(1+i)^n+(1+i)^{n-1}+..+(1+i)</math> : AV of an annuity-due (one period after the date of the last deposit).
<math>\ddot{s}_{\overline{n|}}=(1+i)s_{\overline{n|}}=s_{\overline{n+1|}}-1</math>
<math>a_{\overline{mn|}}=a_{\overline{n|}}+v^n a_{\overline{n|}}+v^{2n} a_{\overline{n|}}+..+v^{(m-1)n} a_{\overline{n|}}</math>
Perpetuities: <math>\lim_{n\to\infty} a_{\overline{n|}} = \lim_{n\to\infty} \frac{1-v^n}{i}=\frac{1}{i}=v+v^2+...= a_{\overline{\infty|}} </math> : PV of a perpetuity-immediate.
<math>\lim_{n\to\infty} \ddot{a}_{\overline{n|}} = \lim_{n\to\infty} \frac{1-v^n}{d}=\frac{1}{d}=1+v+v^2+...= \ddot{a}_{\overline{\infty|}} </math> : PV of a perpetuity-due.
<math>\ddot{a}_{\overline{\infty|}}-a_{\overline{\infty|}}=\frac{1}{d}-\frac{1}{i}=1</math>
My Links
Questions
Feel free to ask me a question here, and I'll do the same.