Two raises, 10% then 10%

Question

Your rent rises 10\% this year and another 10\% next year. Solve in your head. What single increase is this equivalent to? Aim: under 10 seconds.

Accepted Answer

Chain the growth multipliers: 1.10 	imes 1.10 = 1.21. Mental route: 11 	imes 11 = 121, then place the decimal. The rent is 1.21 times the original, so the combined increase is 1.21 - 1 = 21\%. Not 20\%: the second 10\% applies to a base that already grew, adding the +ab = 0.01 compounding bump on top. Takeaway. Successive increases multiply too: (1+a)(1+b) = 1 + a + b + ab. Two 10\% raises give 21\%, not 20\%, because the extra ab = 1\% is interest on the first raise. Compounding always pushes past the naive sum.

Two raises, 10% then 10%

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