Question

section one: background knowledge

1. using percentages

a. what is 3.5% of $400,000?
b. increase $400,000 by 3.5%.
c. increase $400,000 by 3.5% using multiplier.
d. decrease $400,000 by 3.5%.
e. decrease $400,000 by 3.5% using multiplier.

1. convert the following to years.

a. 24 months
b. 30 months
c. 13 weeks
d. 72 weeks

Explanation:

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<reasoning>

Calculate percentage values

We find \(3.5\%\) of \(\$400,000\).
Convert percentage to decimal:
\[3.5\% = 0.035\]
Multiply by the base value:
\[0.035 \times 400,000 = 14,000\]
Thus, \(3.5\%\) of \(\$400,000\) is \(\$14,000\).

Apply percentage increases

For part (b), add the calculated increase to the original amount:
\[400,000 + 14,000 = 414,000\]
For part (c), use the multiplier method.
The multiplier for a \(3.5\%\) increase is:
\[1 + 0.035 = 1.035\]
Multiply the base value:
\[400,000 \times 1.035 = 414,000\]

Apply percentage decreases

For part (d), subtract the calculated decrease from the original amount:
\[400,000 - 14,000 = 386,000\]
For part (e), use the multiplier method.
The multiplier for a \(3.5\%\) decrease is:
\[1 - 0.035 = 0.965\]
Multiply the base value:
\[400,000 \times 0.965 = 386,000\]

Convert months to years

There are 12 months in a year. Divide the number of months by 12.
For part (a):
\[\frac{24}{12} = 2\text{ years}\]
For part (b):
\[\frac{30}{12} = 2.5\text{ years}\]

Convert weeks to years

There are 52 weeks in a year. Divide the number of weeks by 52.
For part (c):
\[\frac{13}{52} = 0.25\text{ years}\]
For part (d):
\[\frac{72}{52} \approx 1.38\text{ years}\]
</reasoning>

<answer>

Question 1

a. \(\$14,000\)
b. \(\$414,000\)
c. \(\$400,000 \times 1.035 = \$414,000\)
d. \(\$386,000\)
e. \(\$400,000 \times 0.965 = \$386,000\)

Question 2

a. \(2\text{ years}\)
b. \(2.5\text{ years}\)
c. \(0.25\text{ years}\) (or \(\frac{1}{4}\text{ year}\))
d. \(\approx 1.38\text{ years}\) (or \(\frac{18}{13}\text{ years}\))
</answer>

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Answer:

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<reasoning>

Calculate percentage values

We find \(3.5\%\) of \(\$400,000\).
Convert percentage to decimal:
\[3.5\% = 0.035\]
Multiply by the base value:
\[0.035 \times 400,000 = 14,000\]
Thus, \(3.5\%\) of \(\$400,000\) is \(\$14,000\).

Apply percentage increases

For part (b), add the calculated increase to the original amount:
\[400,000 + 14,000 = 414,000\]
For part (c), use the multiplier method.
The multiplier for a \(3.5\%\) increase is:
\[1 + 0.035 = 1.035\]
Multiply the base value:
\[400,000 \times 1.035 = 414,000\]

Apply percentage decreases

For part (d), subtract the calculated decrease from the original amount:
\[400,000 - 14,000 = 386,000\]
For part (e), use the multiplier method.
The multiplier for a \(3.5\%\) decrease is:
\[1 - 0.035 = 0.965\]
Multiply the base value:
\[400,000 \times 0.965 = 386,000\]

Convert months to years

There are 12 months in a year. Divide the number of months by 12.
For part (a):
\[\frac{24}{12} = 2\text{ years}\]
For part (b):
\[\frac{30}{12} = 2.5\text{ years}\]

Convert weeks to years

There are 52 weeks in a year. Divide the number of weeks by 52.
For part (c):
\[\frac{13}{52} = 0.25\text{ years}\]
For part (d):
\[\frac{72}{52} \approx 1.38\text{ years}\]
</reasoning>

<answer>

Question 1

a. \(\$14,000\)
b. \(\$414,000\)
c. \(\$400,000 \times 1.035 = \$414,000\)
d. \(\$386,000\)
e. \(\$400,000 \times 0.965 = \$386,000\)

Question 2

a. \(2\text{ years}\)
b. \(2.5\text{ years}\)
c. \(0.25\text{ years}\) (or \(\frac{1}{4}\text{ year}\))
d. \(\approx 1.38\text{ years}\) (or \(\frac{18}{13}\text{ years}\))
</answer>

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