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The Actuarial Nexus
Exam FM Syllabus
1. Time Value of Money (5%-15%)
Learning Objectives
The Candidate will understand and be able to perform calculations relating to present value, current value, and accumulated value.
Learning Outcomes
a) Define and recognize the 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.
b) 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.
c) Given any one of the effective interest rate, the nominal interest rate convertible m-thly, the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, calculate any of the other items.
d) Given any one of the effective interest rate, the nominal interest rate convertible m-thly, the effective discount rate, the nominal discount rate convertible m-thly, or the force of interest, calculate any of the other items.
2. Annuities (20%-30%)
Learning Objectives
The Candidate will be able to calculate present value, current value, and accumulated value for sequences of non-contingent payments.
Learning Outcomes
a) Define and recognize the 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.
b) 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, calculate any remaining item. - Level annuity, finite term. - Level perpetuity. - Non-level annuities/cash flows. - Arithmetic progression, finite term and perpetuity. - Geometric progression, finite term and perpetuity. - Other non-level annuities/cash flows.
3. Loans (15%-25%)
Learning Objectives
The Candidate will understand key concepts concerning loans and how to perform related calculations.
Learning Outcomes
a) Define and recognize the definitions of the following terms: principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization.
b) Calculate: - The missing item, given any four of: term of loan, interest rate, payment amount, payment period, principal. - The outstanding balance at any point in time. - The amount of interest and principal repayment in a given payment. - Similar calculations to the above when refinancing is involved.
4. Bonds (15%-25%)
Learning Objectives
The Candidate will understand key concepts concerning bonds, and how to perform related calculations.
Learning Outcomes
a) Define and recognize the definitions of the following terms: price, book value, market value, amortization of premium, accumulation of discount, redemption value, par value/face value, yield rate, coupon, coupon rate, term of bond, callable/non-callable, call price, call premium, accumulated value with reinvestment of coupons.
b) Given sufficient partial information about the items listed below, calculate any of the remaining items. - Price, book value, market value, accumulated value with reinvestment of coupons, amortization of premium, accumulation of discount. (Note that valuation of bonds between coupon payment dates will not be covered). - Redemption value, face value. - Yield rate. - Coupon, coupon rate. - Term of bond, point in time that a bond has a given book value, amortization of premium, or accumulation of discount.
c) Calculate the price of a callable bond to achieve a specified minimum yield.
5. General Cash Flows, Portfolios, and ALM (20%-30%)
Learning Objectives
The Candidate will understand key concepts concerning yield curves, rates of return, measures of duration and convexity, cash flow matching and immunization, and how to perform related calculations.
Learning Outcomes
a) Define and recognize the definitions of the following terms: yield rate/rate of return, current value, duration and convexity (Macaulay and modified), portfolio, spot rate, forward rate, yield curve, cash flow and duration matching, and immunization (including full immunization and Redington immunization).
b) Calculate: - The duration and convexity of a set of cash flows. - Either Macaulay or modified duration given the other. - The approximate change in present value due to a change in interest rate, - Using 1st-order linear approximation based on modified duration. - Using 1st-order approximation based on Macaulay duration. - The present value of a set of cash flows, using a yield curve developed from forward and spot rates.