A dollar today is worth more than a dollar later, because today's dollar can be invested, while a later dollar loses buying power to inflation and may not arrive at all. This chapter turns that idea into arithmetic: future and present values of single sums, compounding frequency and effective rates, annuities, perpetuities and uneven cash flows. The official study text carries a table of future value interest factors for S$1, so expect calculation questions that give you a factor and test whether you multiply, divide, or pick the right rate and number of periods.
9 sections·~3 min read
✓Checked against the SCI M8 syllabus (exam details page, Contents: Chapter 5 Time Value Of Money and Table 1 Future Value Interest Factors For One Dollar; Objectives: time value of money); MAS MoneySense 'Putting together an investment portfolio' and 'Understanding bonds'; standard compound-interest formulas, all worked figures recomputed, checked 13 Sep 2026. Unofficial prep, not endorsed by MAS or SCI.
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Must-know for the exam
✓Future value of a single sum: FV = PV x (1 + r)^n. The FVIF is (1 + r)^n.
✓Present value of a single sum: PV = FV / (1 + r)^n. PVIF = 1 / FVIF. Given an FVIF, divide; given a PVIF, multiply.
✓Table factors are per PERIOD: 6% a year compounded semi-annually for 4 years uses 3% and 8 periods.
✓Factors for consecutive periods multiply: FVIF(8%, 20 years) = FVIF(8%, 10 years) squared = 2.1589^2 = 4.6608.
✓Effective annual rate: EAR = (1 + r/m)^m - 1. 8% compounded quarterly = 8.24%. EAR equals the nominal rate only with annual compounding.
✓Rule of 72: years to double is about 72 / rate in %. At 9%, about 8 years (exact 8.04). It is an approximation.
✓Annuity due (start-of-period payments): multiply the ordinary annuity value by (1 + r). Same number of payments, each one period earlier.
✓From an FVIF you can get the annuity factor: FV annuity factor = (FVIF - 1) / r.
✓Perpetuity paid at the end of each year: PV = PMT / r. S$2,000 a year at 5% = S$40,000.
✓Uneven cash flows: discount each flow for its own number of periods, then add.
✓NPV = PV of inflows minus cost. Positive: earns more than the required return. Zero: earns exactly the required return, not zero return.
✓Exact real rate = (1 + nominal) / (1 + inflation) - 1. 6% nominal with 2.5% inflation = 3.41%; the shortcut 3.5% slightly overstates it.
✓PV falls when the rate or the time rises. FV rises when the rate or the time rises.
Why money has time value
•Three reasons make a future dollar worth less than a dollar in hand. Opportunity cost: money received now can be invested to earn a return. Inflation: a future dollar buys less. Risk: a promised payment may not arrive.
•The discount rate you apply to future cash flows is your required rate of return. It reflects what you could earn elsewhere at similar risk, so it includes more than inflation.
•Trap: examiners offer tax or bank-charge explanations. They are not the reason. Default risk is a real reason to discount, but it is not what 'opportunity cost' means.
•Takeaway: opportunity cost, inflation and risk. The discount rate is the required return, not just inflation.
Simple versus compound interest
•Simple interest is paid on the original principal only. Compound interest is paid on the principal and on interest already credited, so the interest earned each period grows.
•S$1,000 at 6% compounded: year 1 interest S$60.00, balance S$1,060.00; year 2 interest S$63.60. The extra S$3.60 is interest on interest.
•S$10,000 at 5%: after 10 years simple S$15,000 vs compound S$16,288.95; after 20 years simple S$20,000 vs compound S$26,532.98. The gap widens faster over time.
•Trap: a distractor almost always gives the simple-interest answer, such as 20,000 x (1 + 0.06 x 8) = S$29,600 instead of 20,000 x 1.5938 = S$31,876.
•Takeaway: if the question says compounded, never multiply rate by years. Use (1 + r)^n.
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