The annual interest rate earned by an investment increased by 10 percent from last year to this...

Question

The annual interest rate earned by an investment increased by 10 percent from last year to this year. If the annual interest rate earned by the investment this year was 11 percent, what was the annual interest rate last year?

GMAT Panda · Accepted Answer

10% (Option D) We first create unknowns for last year's and this year's annual interest rates, in percent. r_last = annual rate last year (in percent) r_this = annual rate this year (in percent) We translate "increased by 10 percent" as a relative increase of 10%. r_this = 1.1 r_last We translate "was 11 percent" into an equation for this year's rate. r_this = 11 We solve for r_last by isolating the variable. 11 = 1.1 r_last r_last = 11/1.1 r_last = 11 10/1.1 10 r_last = 110/11 r_last = 11 1011 r_last = 10 We see that r_last = 10, so the rate last year was 10%, corresponding to option D. Answer D

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$We first create unknowns for last year's and this year's annual interest rates, in percent.$	$r_{last} = annual rate last year (in percent) r_{this} = annual rate this year (in percent)$
$We translate "increased by 10 percent" as a relative increase of 10%.$	$r_{this} = 1.1 \times r_{last}$
$We translate "was 11 percent" into an equation for this year's rate.$	$r_{this} = 11$
$We solve for r_{last} by isolating the variable.$	$11 = 1.1 \times r_{last} r_{last} = \frac{11}{1.1} r_{last} = \frac{11 \times 10}{1.1 \times 10} r_{last} = \frac{110}{11} r_{last} = \frac{11 \times 10}{11} r_{last} = 10$
$We see that r_{last} = 10, so the rate last year was 10%, corresponding to option D.$	$Answer D$

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