SOA Exam FM: Financial Mathematics for Actuaries Part 2

Study geometric series and derive finite sum S_n = a(1 - r^n)/(1 - r) for r ≠ 1. Extend to series with limit a/(1 - r) for |r| < 1.

Define annuity immediate as end-of-period payments and derive its present value a-angle n and accumulated value s-angle n, illustrated by rate-based examples and solving for X.

Explain annuity due, where payments begin at time zero, and compute present value a double dot angle n and accumulated value s double dot angle n using i and d.

Explore the present value relationship between annuity immediate and due, including a double dot n equals (1+i) a_n, and distinguish accumulated values s_n from s double dot n using diagrams.

Explore deferred annuities by valuing streams starting in the future using annuity immediate and annuity due, with present value via time diagrams, discounting, and m bar a angle n.

Master annuities with block payments and determine present value and accumulated value with quick shortcut methods. Apply the 5% example to see these techniques in action.

Explore perpetuities, including perpetuity immediate and due, derive present value formulas using infinite geometric series, and apply relationships such as perpetuity due minus perpetuity immediate equals 1, with examples.

Master annuity algebraic relationships, including angle two n over angle n equals one plus v^n. Apply these to solve for i.

Master unknown interest and unknown time problems using calculator methods and algebra. Set up equations of value for annuities, solve for i or n, and apply deferral and perpetuity concepts.

Explore varying interest rates in annuity problems, using time diagrams and equation of value to compute accumulated values for annuities due with rate changes.

Explore valuing annuities with varied payment frequencies by converting rates and using method one or two, including the fission method for quarterly and monthly payments.

Learn annuities with different payment frequencies, including monthly perpetuities and perpetuity due, the M3 trap, annualizing payments, continuous annuities, and essential PV and AV relationships.

Explore the p and q present-value formula for arithmetic progression annuities, derive increasing and decreasing cases, and apply present-value and accumulated formulas for immediate and due annuities.

Study increasing annuities and perpetuities, including increasing perpetuity immediates and due, with p and q annuities and M3 increasing annuities, plus practical examples and proofs.

Learn to value annuities in geometric progression as payments grow with inflation, applying geometric series to present and accumulated values, and relate them to an annuity due with adjusted rate.

Learners explore palindromic annuities, where payments rise to a peak and mirror back. Apply a trick to decompose into annuity streams with angle notation to compute present values at 5%.

explore continuous varying annuities and present value evaluation using calculus, with examples of rates t and t^2 under 4% and 5% effective interest.