Math / Data & Statistics

QuestionSuppose that you have $\$ 14,000$ in a rather risky investment recommended by your financial advisor. During the first year, your investment decreases by $50 \%$ of its original value. During the second year, your investment at the end of year one increases by $60 \%$ . Your advisor tells you that there must have been a $10 \%$ overall increase of your original $\$ 14,000$ investment. Is your financial advisor using percentages properly? If not, what is your actual percent gain or loss of your original $\$ 14,000$ investment?
Select the correct choice below and fill in the answer boxes to complete your choice. (Type a whole number) A. Yes, there is an actual percent loss of $\square$ \% B. No, there is an actual percent loss of $\square$ \% C. Yes, there is an actual percent gain of $\square$ \% D. No, there is an actual percent gain of $\square$ \%

Studdy Solution

STEP 1

What is this asking? Did the investment really grow by 10% after a 50% loss and a 60% gain?
If not, what was the real percentage change? Watch out! Percentages aren't directly added or subtracted, they're multiplicative!
A 50% loss followed by a 50% gain doesn't get you back to even.

STEP 2

1. Calculate the value after the first year.
2. Calculate the value after the second year.
3. Calculate the total percentage change.

STEP 3

Alright, so we start with $\$14{,}000$ .
A 50% decrease means we're losing 50% of that initial value.

STEP 4

To find the loss, we multiply the initial value by the percentage decrease: $\$14{,}000 \cdot 0.50 = \$7{,}000$

STEP 5

So, the value after the first year is the initial value minus the loss: $\$14{,}000 - \$7{,}000 = \$7{,}000$

STEP 6

Now, the investment increases by 60% of its current value, which is $\$7{,}000$ .

STEP 7

The gain in the second year is: $\$7{,}000 \cdot 0.60 = \$4{,}200$

STEP 8

Adding the gain to the value at the beginning of the second year, we get: $\$7{,}000 + \$4{,}200 = \$11{,}200$

STEP 9

The advisor claims a 10% gain, but let's see.
The total change in value is: $\$11{,}200 - \$14{,}000 = -\$2{,}800$ Whoa, that's a negative change, meaning a loss!

STEP 10

To find the percentage change, we divide the total change by the original value and multiply by 100%: $\frac{-\$2{,}800}{\$14{,}000} \cdot 100\% = -0.20 \cdot 100\% = -20\%$ So, there's a 20% loss overall!

STEP 11

No, the advisor is wrong!
The actual change is a loss of 20%, so the answer is B.
No, there is an actual percent loss of 20 %.

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Studdy Solution

STEP 1

What is this asking? Did the investment really grow by 10% after a 50% loss and a 60% gain?
If not, what was the real percentage change? Watch out! Percentages aren't directly added or subtracted, they're multiplicative!
A 50% loss followed by a 50% gain doesn't get you back to even.

STEP 2

1. Calculate the value after the first year.
2. Calculate the value after the second year.
3. Calculate the total percentage change.

STEP 3

Alright, so we start with $\$14{,}000$ .
A 50% decrease means we're losing 50% of that initial value.

STEP 4

To find the loss, we multiply the initial value by the percentage decrease: $\$14{,}000 \cdot 0.50 = \$7{,}000$

STEP 5

So, the value after the first year is the initial value minus the loss: $\$14{,}000 - \$7{,}000 = \$7{,}000$

STEP 6

Now, the investment increases by 60% of its current value, which is $\$7{,}000$ .

STEP 7

The gain in the second year is: $\$7{,}000 \cdot 0.60 = \$4{,}200$

STEP 8

Adding the gain to the value at the beginning of the second year, we get: $\$7{,}000 + \$4{,}200 = \$11{,}200$

STEP 9

The advisor claims a 10% gain, but let's see.
The total change in value is: $\$11{,}200 - \$14{,}000 = -\$2{,}800$ Whoa, that's a negative change, meaning a loss!

STEP 10

To find the percentage change, we divide the total change by the original value and multiply by 100%: $\frac{-\$2{,}800}{\$14{,}000} \cdot 100\% = -0.20 \cdot 100\% = -20\%$ So, there's a 20% loss overall!

STEP 11

No, the advisor is wrong!
The actual change is a loss of 20%, so the answer is B.
No, there is an actual percent loss of 20 %.

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Studdy Solution

STEP 1

What is this asking? Did the investment really grow by 10% after a 50% loss and a 60% gain?If not, what was the real percentage change? Watch out! Percentages aren't directly added or subtracted, they're multiplicative!A 50% loss followed by a 50% gain doesn't get you back to even.

STEP 2

1. Calculate the value after the first year.2. Calculate the value after the second year.3. Calculate the total percentage change.

STEP 3

Alright, so we **start** with $14,000\$14{,}000$14,000.A 50% **decrease** means we're losing 50% of that initial value.

STEP 4

To find the **loss**, we multiply the **initial value** by the **percentage decrease**: $14,000⋅0.50=$7,000 \$14{,}000 \cdot 0.50 = \$7{,}000 $14,000⋅0.50=$7,000

STEP 5

So, the **value** after the first year is the **initial value** minus the **loss**: $14,000−$7,000=$7,000 \$14{,}000 - \$7{,}000 = \$7{,}000 $14,000−$7,000=$7,000

STEP 6

Now, the investment *increases* by 60% of its *current* value, which is $7,000\$7{,}000$7,000.

STEP 7

The **gain** in the second year is: $7,000⋅0.60=$4,200 \$7{,}000 \cdot 0.60 = \$4{,}200 $7,000⋅0.60=$4,200

STEP 8

Adding the **gain** to the **value** at the beginning of the second year, we get: $7,000+$4,200=$11,200 \$7{,}000 + \$4{,}200 = \$11{,}200 $7,000+$4,200=$11,200

STEP 9

The **advisor** claims a 10% **gain**, but let's see.The **total change** in value is: $11,200−$14,000=−$2,800 \$11{,}200 - \$14{,}000 = -\$2{,}800 $11,200−$14,000=−$2,800 Whoa, that's a *negative* change, meaning a **loss**!

STEP 10

STEP 11

No, the advisor is wrong!The actual change is a **loss** of 20%, so the answer is B.No, there is an actual percent loss of **20** %.

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Studdy solves anything!

Start learning now

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What is this asking? Did the investment really grow by 10% after a 50% loss and a 60% gain?
If not, what was the real percentage change? Watch out! Percentages aren't directly added or subtracted, they're multiplicative!
A 50% loss followed by a 50% gain doesn't get you back to even.

1. Calculate the value after the first year.
2. Calculate the value after the second year.
3. Calculate the total percentage change.

Alright, so we start with $\$14{,}000$ .
A 50% decrease means we're losing 50% of that initial value.

To find the loss, we multiply the initial value by the percentage decrease: $\$14{,}000 \cdot 0.50 = \$7{,}000$

So, the value after the first year is the initial value minus the loss: $\$14{,}000 - \$7{,}000 = \$7{,}000$

Now, the investment increases by 60% of its current value, which is $\$7{,}000$ .

The gain in the second year is: $\$7{,}000 \cdot 0.60 = \$4{,}200$

Adding the gain to the value at the beginning of the second year, we get: $\$7{,}000 + \$4{,}200 = \$11{,}200$

The advisor claims a 10% gain, but let's see.
The total change in value is: $\$11{,}200 - \$14{,}000 = -\$2{,}800$ Whoa, that's a negative change, meaning a loss!

No, the advisor is wrong!
The actual change is a loss of 20%, so the answer is B.
No, there is an actual percent loss of 20 %.