Financial Mathematics

Payments continue forever, Present value can be calculated, Uses formula P = R/i

A perpetuity has infinite payments, calculable present value, undefined future amount, and no maturity date. The present value formula is P = R/i. Common misconception: thinking perpetuities have maturity dates.

10%

CAGR = [(EV/SV)^(1/n) - 1] × 100 = [(16,105/10,000)^(1/5) - 1] × 100 = [(1.6105)^0.2 - 1] × 100 = [1.10 - 1] × 100 = 10%. Common error: Using simple average instead of geometric mean.

₹877

Bond value = R[1-(1+i)⁻ⁿ]/i + F(1+i)⁻ⁿ. Here R = 80, i = 0.10, n = 10, F = 1000. Present value of annuity = 80 × 6.1446 = ₹491.57. Present value of principal = 1000 × 0.3855 = ₹385.54. Total = ₹877.11 ≈ ₹877. Common mistake: Using coupon rate instead of yield rate for discounting.

₹9,000

Annual depreciation = (Cost - Scrap value)/Useful life = (80,000 - 8,000)/8 = 72,000/8 = ₹9,000. This method provides uniform annual depreciation. Common error: Including scrap value in depreciation or dividing by wrong number of years.