Financial Mathematics

This course presents the fundamental principles of financial mathematics, as applied in the fixed income departments of banks and in the life insurance and pensions businesses.  The syllabus exactly follows the first part of the 2015 syllabus of the financial mathematics exam of the Society of Actuaries (the second part of this latter exam is about derivatives and is not covered). See This syllabus is as follows.

“Definitions of the following terms: interest rate (rate of interest), simple interest, compound interest, accumulation function, future value, current value, present value, net present value, discount factor, discount rate (rate of discount), convertible m-thly, nominal rate, effective rate, inflation and real rate of interest, force of interest, equation of value. Given any three of interest rate, period of time, present value and future value, calculate the remaining item using simple or compound interest. Solve time value of money equations involving variable force of interest. Given the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, calculate any of the other items. Write the equation of value given a set of cash flows and an interest rate.

Definitions of the following terms: annuity-immediate, annuity due, perpetuity, payable m-thly or payable continuously, level payment annuity, arithmetic increasing/decreasing annuity, geometric increasing/decreasing annuity, term of annuity. For each of the following types of annuity/cash flows, given sufficient information of immediate or due, present value, future value, current value, interest rate, payment amount, and term of annuity, the candidate will be able to calculate any remaining item. Arithmetic progression, finite term. Level annuity, finite term. Arithmetic progression, perpetuity. Level perpetuity. Geometric progression, finite term. Non-level annuities/cash flows. Geometric progression, perpetuity. Other non-level annuities/cash flows.

Definitions of the following terms: principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, sinking fund. Given any four of term of loan, interest rate, payment amount, payment period, principal, calculate the remaining item. Calculate the outstanding balance at any point in time. Calculate the amount of interest and principal repayment in a given payment. Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.”