# Compound Interest

An asset of original value P that appreciates at rate r every period is worth, after t period $$V = P \left( 1 + r \right)^{t}$$

## Example

You bought a pair of sneakers 100. Every year, it value increases by %5.

• After 1 year, the sneakers are worth \$100 \times \left( 1 + 5\% \right) = \$105
• After 2 years, the sneakers are worth \$100 \times \left( 1 + 5\% \right) \times \left( 1 + 5\% \right) = \$100 \times \left( 1 + 5\% \right)^{2} = \$110.25 • After 3 years, the sneakers are worth \$100 \times \left( 1 + 5\% \right) \times \left( 1 + 5\% \right) \times \left( 1 + 5\% \right) = \$100 \times \left( 1 + 5\% \right)^{3} \approx \$115.76
• and so on

### Question

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