How to find the average compound interest for all years, knowing the starting and ending values, as well as the number of years

Question

For example:

Company X shares in 2016 - 38 USD

5 years later, in 2021 - 66.95 USD

38 + 12% (4.56 USD) + 12% (5.10 USD) + 12% (5.72 USD) + 12% (6.40 USD) + 12% (7.17 USD) = 66.95 USD

What formula should I use to know that the average compound interest is 12% for each year?

Answer 1

We have:

$38(1+0.12)^5=66.96$

The general formula is:

$S=S_1(1+i)^n$

Where $S_1$ is initial investment, i is interest rate and n is number of years for investment. Total compound interest rate is:

$I=(1+0.12)^5-1=0.762$

The average rate of interest is:

$\frac{0.762}5=0.152=15.2$%

Answer 2

Compound interest formula with unknown interest rate is:

CI = ((FV / PV)^(1/n) − 1) * 100

Where:

• CI - AVG Compound Interest (what we need to find)
• FV - Future Value (66.95)
• PV = Present Value (38)
• n = Number of Periods (5 years)

What we got:

((66.95 / 38)^1/5 − 1) * 100 = 11,9969 (AVG %)