Financial Mathematics (FM) Exam
Interest theory
Financial Mathematics questions center on dated cash flows. Master accumulation and discount factors, effective and nominal rates, force of interest, annuities, perpetuities, loans, bonds, and yield rates. Convert nominal rates carefully: a nominal rate compounded m times per year has per-period rate i^(m)/m. For continuous compounding, use e^(delta t). Draw a timeline and place every cash flow at the correct time before choosing a formula.
Annuities, loans, and bonds
Distinguish annuity-immediate from annuity-due. The due version multiplies the immediate value by (1+i). For loans, the outstanding balance equals the present value of remaining payments or the original loan accumulated with interest minus accumulated payments. For bonds, price equals the present value of coupons plus redemption value; premium or discount depends on coupon rate versus yield. Duration and convexity measure interest-rate sensitivity, but duration is not a complete hedge for large rate changes.
Worked rule
Find the present value at time 0 of 100 paid at the end of each year for 10 years at 5%. PV = 100 a-angle-10 at 5% = 100(1 - 1.05^-10)/0.05 = 772.17. If payments are at the beginning of each year, multiply by 1.05 to get 810.78. The trap is mixing the timing convention with the rate convention. Write the annuity symbol and its timing before substituting numbers.