Financial Mathematics: Compound Interest, Annuities, and Loans
Core concepts
Financial Mathematics on this exam centres on the time value of money. You must be fluent with compound interest, where a balance grows by a fixed multiplier each period: (A = P(1+i)^n), with (i) the interest rate per compounding period and (n) the total number of periods. When compounding frequency differs from the payment frequency you must convert the nominal annual rate to a periodic rate, and when payments occur more often than compounding you need an equivalent rate rather than simply dividing.
You also need the annuity formulas. For an ordinary annuity (payments at period end), the future value is (FV = R\frac{(1+i)^n-1}{i}) and the present value is (PV = R\frac{1-(1+i)^{-n}}{i}). A loan is a present-value annuity: the loan amount equals the present value of all payments. The outstanding balance after (k) payments is the present value of the remaining payments.
Traps to watch
- Mixing annual and monthly rates without converting. Always match the rate, the number of periods, and the payment timing.
- Forgetting that payments at the beginning of a period (annuity due) multiply the ordinary result by ((1+i)).
- Rounding intermediate values too early, which shifts final answers by dollars.
- Misreading "how much interest is paid" versus "total paid" versus "outstanding balance."
Rule of thumb
Draw a timeline: mark deposits as arrows up, withdrawals as arrows down, and put the focal date at the point you are valuing. Every problem becomes a sum of moved amounts.
Worked example
$500 is deposited monthly at 6% per year compounded monthly for 10 years. (i=0.005), (n=120). (FV = 500\frac{(1.005)^{120}-1}{0.005} \approx 500(163.879) \approx $81{,}940).