Chapter 2. Time Value of Money

PV = FV ÷ (1 + r)ⁿ

Excel: PV(rate, nper, 0, −FV)

Example →

₹50,000 receivable after 5 years at 6% → 50,000 ÷ 1.06⁵ = ₹37,362.91.

Trap →

The rate is stated 'quarterly' but the term is in years. Convert first: r = 6% ÷ 4 = 1.5%, n = 5 × 4 = 20.

PV = C × [1 − (1 + r)⁻ⁿ] ÷ r

Excel: PV(rate, nper, −C)

Example →

Shyam gets ₹6,500 a year for 8 years at 7% → 6,500 × 5.9713 = ₹38,813.44.

Trap →

'Payments at the start of each year' makes it an annuity due: multiply the result by (1 + r), or use type = 1 in Excel.

FV = PV × (1 + r)ⁿ

Excel: FV(rate, nper, 0, −PV)

Example →

Krishna invests ₹5,00,000 at 8% for 5 years, compounded annually → ₹7,34,664 (interest ₹2,34,664).

Trap →

The same problem compounded quarterly (r = 2%, n = 20) gives ₹7,42,974. Watch for the compounding frequency hidden in the question.

CAGR = (End value ÷ Begin value)^(1/n) − 1

Excel: RATE(n, 0, −Begin, End)

Example →

NAV grows from ₹10.50 to ₹12.25 in 3 years → (12.25 ÷ 10.50)^(1/3) − 1 = 5.27%.

Trap →

For periods under one year CAGR isn't appropriate; use the simple (absolute) return. Fractional years are fine, e.g. n = 450/365.

EMI = P × r × (1 + r)ⁿ ÷ [(1 + r)ⁿ − 1] (r monthly, n months)

Excel: PMT(rate/12, years×12, −loan)

Example →

₹30 lakh loan at 6.5% for 20 years → PMT(0.065/12, 240, −30,00,000) = ₹22,367 a month.

Trap →

If the rate is already given as a monthly rate (e.g. 0.6% a month), don't divide by 12 again. Enter the loan as negative to get a positive EMI.

Number of periods needed to repay a loan at a given EMI

Excel: NPER(rate/12, −EMI, loan)

Example →

₹5,00,000 loan, EMI ₹12,000, rate 8% → NPER(0.08/12, −12000, 500000) = 48.98 months.

Trap →

The answer comes out in months; if the question asks for years, convert (48.98 ÷ 12 ≈ 4.08 years).

Principal part = PPMT(rate, period, nper, pv) · Interest part = IPMT(rate, period, nper, pv)

Excel: PPMT(0.07/12, 1, 120, −1000000) · IPMT(0.07/12, 1, 120, −1000000)

Example →

₹10 lakh at 7% for 10 years, month 1 → EMI ₹11,611 = interest ₹5,833 + principal ₹5,778. Interest dominates early EMIs.

Trap →

'A higher rate means more of the EMI goes to principal early' is wrong. A higher rate raises the interest share of early EMIs.

PV(due) = PV(ordinary) × (1 + r)

Excel: type = 0 (end of period) vs type = 1 (start of period)

Example →

₹5,000 a year for 4 years at 10% → ordinary ₹15,849.33; annuity due ₹17,434.26.

Trap →

Rent paid at the start of the month is an annuity due (higher PV); salary received at month-end is an ordinary annuity.

PV = C ÷ r

Example →

A perpetual bond paying ₹10,000 a year at an 8% discount rate → 10,000 ÷ 0.08 = ₹1,25,000.

Trap →

A 'very long-term 50-year bond' is still an annuity, not a perpetuity. A perpetuity has no n.