3.3 Compound Discount

3.3.1 Compound Discount at a Discount Rate

Let d^m be the nominal rate of discount compounded m times per year.

Then the discount rate per conversion period is d^m/m and the discounted value 𝑃 of a future amount 𝑆 due in 𝑛 periods is

(1) $\begin{equation*} P = S(1 - \frac{{d}^{m}}{m})^{n} \end{equation*}$

Thus, the accumulated value $S$ is:

(2) $\begin{equation*} S = P(1 - \frac{{d}^{m}}{m})^{-n} \end{equation*}$

Example 3.5

Find the discounted value of RM1000 due in 2 years at d =12% compounded monthly.

Example 3.6

Find the discounted value of RM1000 due in 2 years at d=7% compounded daily.