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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?

Explanation	Calculations	Help
$We first create unknowns for last year's and this year's annual interest rates, in percent.$	$r_{last} = annual rate last year (in percent) r_{this} = annual rate this year (in percent)$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "increased by 10 percent" as a relative increase of 10%.$	$r_{this} = 1.1 \times r_{last}$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "was 11 percent" into an equation for this year's rate.$	$r_{this} = 11$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We solve for r_{last} by isolating the variable.$	$11 = 1.1 \times r_{last} r_{last} = \frac{11}{1.1} r_{last} = \frac{11 \times 10}{1.1 \times 10} r_{last} = \frac{110}{11} r_{last} = \frac{11 \times 10}{11} r_{last} = 10$
$We see that r_{last} = 10, so the rate last year was 10%, corresponding to option D.$	$Answer D$

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10% (Option D)

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?

Explanation	Calculations	Help
$We first create unknowns for last year's and this year's annual interest rates, in percent.$	$r_{last} = annual rate last year (in percent) r_{this} = annual rate this year (in percent)$	Theory & Tactics Method Card TRANS1-A Click to view full details
$We translate "increased by 10 percent" as a relative increase of 10%.$	$r_{this} = 1.1 \times r_{last}$	Theory & Tactics Method Card TRANS2-D Click to view full details
$We translate "was 11 percent" into an equation for this year's rate.$	$r_{this} = 11$	Theory & Tactics Method Card TRANS1-B Click to view full details
$We solve for r_{last} by isolating the variable.$	$11 = 1.1 \times r_{last} r_{last} = \frac{11}{1.1} r_{last} = \frac{11 \times 10}{1.1 \times 10} r_{last} = \frac{110}{11} r_{last} = \frac{11 \times 10}{11} r_{last} = 10$
$We see that r_{last} = 10, so the rate last year was 10%, corresponding to option D.$	$Answer D$

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10% (Option D)