1985 AJHSME Problem 21

Problem

Mr. Green receives a $10\%$ raise every year. His salary after four such raises has gone up by what percent?

$\text{(A)}\ \text{less than }40\% \qquad \text{(B)}\ 40\% \qquad \text{(C)}\ 44\% \qquad \text{(D)}\ 45\% \qquad \text{(E)}\ \text{more than }45\%$

Solution

If Mr. Green's original salary is $100, then his salary after four raises is $(100)(1.1)^4 = 146.41.$ This is an increase of 46.41%, so the answer is $\text{(E)}\ \text{more than }45\%.$

(note: this number can be calculated by recalling powers of $11$ appear in Pascal's Triangle: $11^4$ appears on the fourth row, which is $1 4 6 4 1$ meaning that $11^4=14641$ , so $1.1^4=1.4641$ .

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1985 AJHSME Problem 21

Problem

Solution