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Time Value of Money Example

Easy DifficultyFE Engineering Economics

Find the future worth of a present sum and the present worth of a future sum using compound interest (equivalence).

Concept

Time value of money : a dollar today is worth more than a dollar in the future because of interest. With compound interest rate i per period, a present amount P grows to a future amount F after n periods. Conversely, the present worth of a future amount F is P = F (1 + i)^{- n} . F = P (1 + i)^{n} or F = P (F / P, i, n) P = F (1 + i)^{- n} = \frac{F}{( 1 + i ) ^{n}} or P = F (P / F, i, n) Notation: P = present worth, F = future worth, i = interest rate per period, n = number of periods.

(1) You invest P = $10, 000 today at 6% per year compounded annually. What is the future worth after 5 years? (2) A payment of F = $15, 000 is due in 4 years. If the interest rate is 6% per year, what is the present worth of that payment today?

Part 1: P = $10, 000, i = 6% = 0.06, n = 5 years Part 2: F = $15, 000, i = 0.06, n = 4 years

F = P (1 + i)^{n} or F = P (F / P, i, n) F = 10, 000 (1.06)^{5} = 10, 000 \times 1.3382 \approx 13, 382

P = F (1 + i)^{- n} = \frac{F}{( 1 + i ) ^{n}} or P = F (P / F, i, n) P = \frac{15 , 000}{( 1.06 ) ^{4}} = \frac{15 , 000}{1.2625} \approx 11, 881

(1) Future worth after 5 years: F \approx $13, 382 (2) Present worth of $15,000 in 4 years: P \approx $11, 881

F = P (1 + i)^{n}, P = F (1 + i)^{- n} Notation: P = present worth, F = future worth, i = interest rate per period, n = number of periods. Tables give (F / P, i, n) and (P / F, i, n) .