Question

find the simple interest earned to the nearest cent for each principal, interest rate, and time.

	principal	annual interest rate	time	simple interest
8.		4.25%	3 months	$7.65
9.	$2,500	6.9%		$86.25
10.	$500		18 months	$90

1. rita charged $126 for a dvd player at an interest rate of 15.9%. how much will rita have to pay after 2 months if she makes no payments?

1. the average cost for a vacation is $1,050. if a family borrows money for the vacation at an interest rate of 11.9% for 6 months, what is the total cost of the vacation including the interest on the loan?

1. when melissa was born, her parents put $8,000 into a college fund and earned $12,960 after 18 years. find the interest rate for melissa’s account. find the total of her account after 18 years.

Explanation:

Step1: Recall simple interest formula

The simple interest formula is $I = P \times r \times t$, where $I$ = interest, $P$ = principal, $r$ = annual interest rate (decimal), $t$ = time in years. Total amount owed/paid is $A = P + I$.

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Problem 7

Step1: Identify values

$P = 668$, $r = 0.05$, $t = 2$

Step2: Calculate simple interest

$I = 668 \times 0.05 \times 2 = 66.80$

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Problem 8

Step1: Identify values

$I = 7.65$, $r = 0.0425$, $t = \frac{3}{12} = 0.25$

Step2: Solve for principal $P$

$P = \frac{I}{r \times t} = \frac{7.65}{0.0425 \times 0.25} = 720$

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Problem 9

Step1: Identify values

$P = 2500$, $r = 0.069$, $I = 86.25$

Step2: Solve for time $t$

$t = \frac{I}{P \times r} = \frac{86.25}{2500 \times 0.069} = 0.5$ years (6 months)

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Problem 10

Step1: Identify values

$P = 500$, $I = 90$, $t = \frac{18}{12} = 1.5$

Step2: Solve for rate $r$

$r = \frac{I}{P \times t} = \frac{90}{500 \times 1.5} = 0.12$ or 12%

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Problem 11

Step1: Identify values

$P = 126$, $r = 0.159$, $t = \frac{2}{12} = \frac{1}{6}$

Step2: Calculate interest

$I = 126 \times 0.159 \times \frac{1}{6} \approx 3.34$

Step3: Calculate total amount owed

$A = 126 + 3.34 = 129.34$

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Problem 12

Step1: Identify values

$P = 1050$, $r = 0.119$, $t = \frac{6}{12} = 0.5$

Step2: Calculate interest

$I = 1050 \times 0.119 \times 0.5 = 62.48$

Step3: Calculate total cost

$A = 1050 + 62.48 = 1112.48$

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Problem 13

Step1: Calculate earned interest

$I = 12960 - 8000 = 4960$

Step2: Identify values

$P = 8000$, $I = 4960$, $t = 18$

Step3: Solve for rate $r$

$r = \frac{I}{P \times t} = \frac{4960}{8000 \times 18} \approx 0.0344$ or 3.44%

Step4: State total account value

Total amount = $12,960$ (given)

Answer:

1. $\$66.80$
2. $\$720$
3. 0.5 years (6 months)
4. 12%
5. $\$129.34$
6. $\$1112.48$
7. Interest rate: ~3.44%; Total account amount: $\$12,960$