Question

a. traub deposited $510 into an account. after 2 years, his balance was $945. what was his rate? b. kay deposited $675 into an account. after 3 years, her balance was $975. what was her rate?

Explanation:

We assume this is simple interest, using the formula $A = P(1 + rt)$, where:

• $A$ = final amount, $P$ = principal, $r$ = annual interest rate, $t$ = time in years

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Part a

Step1: List given values

$P = 510$, $A = 945$, $t = 2$

Step2: Rearrange formula for $r$

$r = \frac{\frac{A}{P} - 1}{t}$

Step3: Substitute values

$r = \frac{\frac{945}{510} - 1}{2}$

Step4: Calculate numerator first

$\frac{945}{510} - 1 = \frac{945 - 510}{510} = \frac{435}{510} \approx 0.8529$

Step5: Divide by time

$r = \frac{0.8529}{2} \approx 0.4265$ or $42.65\%$

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Part b

Step1: List given values

$P = 675$, $A = 975$, $t = 3$

Step2: Use rearranged $r$ formula

$r = \frac{\frac{A}{P} - 1}{t}$

Step3: Substitute values

$r = \frac{\frac{975}{675} - 1}{3}$

Step4: Calculate numerator first

$\frac{975}{675} - 1 = \frac{975 - 675}{675} = \frac{300}{675} \approx 0.4444$

Step5: Divide by time

$r = \frac{0.4444}{3} \approx 0.1481$ or $14.81\%$

Answer:

a. Approximately $42.65\%$
b. Approximately $14.81\%$