Financial Math for Actuaries, Lec 2: Valuation of Annuities (Level, Varying, Discrete, & Continuous)

Annuities arise in various kinds of financial transactions, such as loan payments, bond coupon payments, and insurance premium payments. Learn how to find their present and future values. TI BAII Plus Calculator: https://amzn.to/2Mmk4f6. Mathematics of Investment and Credit, 6th Edition, by Samuel Broverman: https://amzn.to/2s9SZEQ. Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. Check out my blog: https://infinityisreallybig.com/. Playlist for problems on valuation of annuities:    • Actuarial Exam 2/FM Prep: Find the In...  

(0:00) Introduction
(0:15) Graph and interpret (1+i)^t and v^t, where v=(1+i)^(-1) (for various values of the interest rate i)
(3:53) Graph and interpret v=1/(1+i)=1-d, where d is the effective periodic discount rate
(5:45) Graph and interpret d=i/(1+i) and its inverse function i=d/(1-d)
(7:34) Graph and interpret i=1/v-1=(1-v)/v
(9:38) Finite geometric series formula in symbols and in words (using the first term, common ratio, and number of terms)
(12:53) Sum of a convergent infinite geometric series in symbols and words
(13:44) What is an annuity? They can be level or varying. They can be discrete or continuous. They can start at any point in time.
(15:44) Level annuity immediate (with n payments)
(18:45) Level annuity due (with n payments)
(21:01) Find the future value (accumulated value) of an annuity immediate, including the actuarial notation.
(24:59) AV of an annuity due
(27:45) Present values and notation of annuities-immediate and annuities-due
(31:37) Deferred annuities
(35:21) Equations should be understood intuitively as well as derived algebraically
(37:52) Present values of perpetuities (annuities that go on perpetually (forever)), including deferred perpetuities
(40:09) Geometrically increasing annuities
(43:04) Arithmetically increasing annuities (more common)
(45:25) Arithmetically decreasing annuities
(47:06) Continuous annuities (a.k.a. cash flows or payment streams) using a force of interest function (formulas involve definite integrals)
(51:30) Use a force of interest
(53:03) Level continuous annuities (constant interest rate)
(55:31) Continuously increasing annuities
(57:47) Continuously decreasing annuities
(59:07) Conclusion

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