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:

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):

$$\frac{72}{52} \approx 1.38\text{ years}$$

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 \(\frac{18}{13}\text{ years}\))