Question

1. use the simple interest formula to find the missing entries in the table. round monetary amounts to the nearest cent.

interest

principal

rate to the nearest hundredth of a percent

time

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-----------

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a.

$2,000

3.35%

4 years

b.

$3,500

4.1%

15 months

c.

$20,100

5.5%

400 days

$100

$700

8.8%

d.

$250

$3,000

$4\frac{3}{4}%$

e.

$500

$3,000

f.

3 years

$500

g.

4.4%

30 months

x

p

3%

h.

Explanation:

The simple interest formula is $I = P \times r \times t$, where:

• $I$ = Interest
• $P$ = Principal
• $r$ = annual interest rate (decimal form)
• $t$ = time in years

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Step1: Solve for a. (Find I)

Convert rate to decimal: $3.35\% = 0.0335$
Time is already in years.
$I = 2000 \times 0.0335 \times 4$
$I = 2000 \times 0.134 = 268$

Step2: Solve for b. (Find I)

Convert rate to decimal: $4.1\% = 0.041$
Convert months to years: $t = \frac{15}{12} = 1.25$
$I = 3500 \times 0.041 \times 1.25$
$I = 3500 \times 0.05125 = 179.375$

Step3: Solve for c. (Find I)

Convert rate to decimal: $5.5\% = 0.055$
Convert days to years: $t = \frac{400}{365}$
$I = 20100 \times 0.055 \times \frac{400}{365}$
$I = 20100 \times 0.055 \times 1.09589 \approx 1210.68$

Step4: Solve for d. (Find r)

Rearrange formula: $r = \frac{I}{P \times t}$
Convert days to years: $t = \frac{400}{365}$
$r = \frac{100}{700 \times \frac{400}{365}} = \frac{100 \times 365}{700 \times 400} = \frac{36500}{280000} \approx 0.1304$
Convert to percent: $0.1304 \times 100 = 13.04\%$

Step5: Solve for e. (Find t)

Rearrange formula: $t = \frac{I}{P \times r}$
Convert rate to decimal: $4\frac{3}{4}\% = 4.75\% = 0.0475$
$t = \frac{250}{3000 \times 0.0475} = \frac{250}{142.5} \approx 1.75$ years

Step6: Solve for f. (Find P)

Rearrange formula: $P = \frac{I}{r \times t}$
Convert rate to decimal: $4.4\% = 0.044$
$P = \frac{500}{0.044 \times 3} = \frac{500}{0.132} \approx 3787.88$

Step7: Solve for g. (Find I)

Convert rate to decimal: $4.4\% = 0.044$
Convert months to years: $t = \frac{30}{12} = 2.5$
$I = 3000 \times 0.044 \times 2.5$
$I = 3000 \times 0.11 = 330$

Step8: Solve for h. (Find r)

Rearrange formula: $r = \frac{I}{P \times t}$
Convert months to years: $t = \frac{30}{12} = 2.5$
$r = \frac{500}{P \times 2.5}$
Wait, correction: For h, $I=500$, $P=x$ (unknown), $r=3\%=0.03$, $t=30$ months $=2.5$ years.
Rearrange to find $P$: $P = \frac{I}{r \times t} = \frac{500}{0.03 \times 2.5} = \frac{500}{0.075} \approx 6666.67$

Answer:

Interest	Principal	Rate (percent)	Time
b. $\$179.38$	$\$3,500$	4.1%	15 months
c. $\$1,210.68$	$\$20,100$	5.5%	400 days
d. $\$100$	$\$700$	13.04%	400 days
e. $\$250$	$\$3,000$	$4\frac{3}{4}\%$	1.75 years
f. $\$500$	$\$3,787.88$	4.4%	3 years
g. $\$330.00$	$\$3,000$	4.4%	30 months
h. $\$500$	$\$6,666.67$	3%	30 months