FORMULABANK

Interest / Growth Rate in % (r)

When you want to determine the interest rate or the growth rate per period and you know the initial value, final value, and number of periods.

The formula is as follows:

$r=\sqrt[n]{\frac{F_n}{F_0}}-1$

• F_n = Final capital / final value
• F₀ = Initial capital / initial value
• r = Interest / growth rate in % per period
• n = Number of periods

Example:

In Freemont  Water Polo Club, there were 85 members in 2000 and 154 members in 2017.

The number of periods is  [insert number of periods here].

Calculation Example:

Using the formula:

$r=\sqrt{17\cdot \frac{154}{85}}-1\approx 0.03557715$

Alternatively:

$154=85\cdot (1+x)$¹⁷

The equation is solved for x using the CAS tool WordMat:

$r=0.0355771485$

Therefore, there has been a growth of approximately 3.56% per year.