# Compound Interest - Example - Find Rate

The interest rate necessary to reach a value G after t periods from an asset of value P is $$r = \left( \frac{G}{P} \right)^{\frac{1}{t}} -1$$

## Example

You have placed \$1000 in your savings account. You hope that your capital will reach$1500 in 10 years. The rate r solves \begin{align*} 1000 \left( 1 + r \right)^{10} &= 1500 \\ \left( 1 + r \right)^{10} &= \frac{1500}{1000} \\ 1 + r &= \left( \frac{1500}{1000} \right)^{\frac{1}{10}} \\ r &= \left( \frac{1500}{1000} \right)^{\frac{1}{10}} - 1 \\ r &\approx 0.0414 \end{align*} The interest rate has to be 4.14%.

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