Present and Future Value Math Example 4

Follow the full solution, then compare it with the other examples linked below.

Example 4

hard
Compare the future values of \10{,}000investedfor invested for 20yearsat years at 6\%$ with (a) annual compounding, (b) monthly compounding, and (c) continuous compounding.

Solution

  1. 1
    (a) FV = 10000(1.06)^{20} \approx \32{,}071.(b). (b) FV = 10000(1+0.005)^{240} \approx 10000(3.3102) \approx \33,10233{,}102. (c) FV = 10000 \cdot e^{0.06 \times 20} = 10000 \cdot e^{1.2} \approx 10000(3.3201) \approx \33{,}201$.
  2. 2
    Monthly compounding earns \1{,}031morethanannual;continuousearns more than annual; continuous earns \9999 more than monthly.

Answer

(a) $32,071(b) $33,102(c) $33,201\text{(a) } \$32{,}071 \quad \text{(b) } \$33{,}102 \quad \text{(c) } \$33{,}201
More frequent compounding produces higher future values because interest is earned on interest sooner. The gap between annual and monthly compounding is significant, but the gap between monthly and continuous is small — showing diminishing returns from increasing compounding frequency.

About Present and Future Value

The concept that money has different values at different points in time. Future value (FVFV) calculates what a present amount will grow to; present value (PVPV) calculates what a future amount is worth today, using discounting.

Learn more about Present and Future Value →

More Present and Future Value Examples

Example 1 easy

Find the future value of [formula]5{,}000[formula]4%[formula]6$ years.

Example 2 medium

How much should you invest today at [formula] annual interest compounded quarterly to have [formula]

Example 3 medium

An investment doubles in [formula] years with annual compounding. What is the approximate annual int

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