Present and Future Value Math Example 3

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

Example 3

medium
An investment doubles in 99 years with annual compounding. What is the approximate annual interest rate?

Solution

  1. 1
    FV=2⋅PVFV = 2 \cdot PV, so 2=(1+r)92 = (1+r)^9. Take the 9th root: 1+r=21/91 + r = 2^{1/9}.
  2. 2
    r=21/9−1≈1.0801−1=0.0801≈8.01%r = 2^{1/9} - 1 \approx 1.0801 - 1 = 0.0801 \approx 8.01\%.

Answer

r≈8%r \approx 8\%
The Rule of 72 provides a quick estimate: 72/9=8%72 / 9 = 8\%, which matches our exact calculation closely. To find the rate when you know the doubling time, use r=21/n−1r = 2^{1/n} - 1. This demonstrates the power of compound growth.

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 4 hard

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

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