Present and Future Value Math Example 2

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

Example 2

medium
How much should you invest today at 5%5\% annual interest compounded quarterly to have \20{,}000in in 8$ years?

Solution

  1. 1
    Use the present value formula: PV=FV(1+r)nPV = \frac{FV}{(1 + r)^n}.
  2. 2
    Quarterly rate: r=0.054=0.0125r = \frac{0.05}{4} = 0.0125. Total periods: n=4ร—8=32n = 4 \times 8 = 32.
  3. 3
    (1.0125)32โ‰ˆ1.4881(1.0125)^{32} \approx 1.4881.
  4. 4
    PV = \frac{20000}{1.4881} \approx \13{,}440.09$.

Answer

โ‰ˆ$13,440\approx \$13{,}440
Present value is the current worth of a future amount, discounted by the interest rate. It answers the question: 'How much do I need to invest now?' Quarterly compounding means the rate is divided by 4 and the number of periods is multiplied by 4.

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 โ†’

More Present and Future Value Examples

Example 1 easy

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

Example 3 medium

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

Example 4 hard

Compare the future values of [formula]10{,}000[formula]20[formula]6%$ with (a) annual compounding, (

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