Question:
How much would $5,000 due in 20 years be worth today if the discount rate was 5.0%?
Present Value:
The idea of the time value of money is useful in figuring out the equivalent present worth of an expected future amount. It takes into account the factors such as the applicable interest rate, compounding interval, and time till maturity.
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The calculated present worth of $5,000 due in 20 years is $1,884.45.
The present value of the investment is given by:
{eq}\begin{align*}&= \dfrac{\text{Amount due in 5 years}}{\text{(1 + discount rate)} ^ {\text{Number of years}}} \\[0.3 cm]&= \dfrac{\$5,000}{(1 + 5\%)^{20}}\\[0.3 cm]&= \dfrac{\$5,000}{(1.05)^{20}} \\[0.3 cm]&= \$1,884.45 \\[0.3 cm]\end{align*}{/eq}
