1985 AJHSME Problems/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

Assume his salary is originally $100$ dollars. Then, in the next year, he would have $110$ dollars, and in the next, he would have $121$ dollars. The next year he would have $133.1$ dollars and in the final year, he would have $146.41$ . As the total increase is greater than $45\%$ , the answer is $\boxed{\text{E}}$ .

~sakshamsethi

Solution 2

Let Mr.Green's salary be $x$ dollars.

Notice Mr.Green's salary is a geometric sequence with common ratio $\frac{11}{10}$

Apply the general term formula for geometric sequences, after four years, Mr.Green's salary becomes $x \cdot (\frac{11}{10})^4$ which is $\frac{14641}{10000}x$ .

$\frac{4641}{10000}$ is more than $45\%$ , thus the answer is $\boxed{\textbf{(E)}\ more than 45\%}$

1985 AJHSME (Problems • Answer Key • Resources)
Preceded by Problem 20	Followed by Problem 22
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1985 AJHSME Problems/Problem 21

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Problem

Solution

Solution 2

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