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

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