Math / Algebra

QuestionSuppose your salary in 2013 is $\$ 65,000$ . If the annual inflation rate is $4 \%$ , what salary do you need to make in 2022 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary. Formulas

Studdy Solution

STEP 1

What is this asking? How much money do we need to make in 2022 to have the same buying power as $\$65,000$ in 2013, given a $\$4\%$ yearly inflation? Watch out! Don't forget that salaries grow exponentially with inflation, not linearly!

STEP 2

1. Calculate the number of years.
2. Calculate the equivalent salary.

STEP 3

Let's figure out how many years have passed between 2013 and 2022.
It's as simple as subtracting the earlier year from the later year: $2022 - 2013 = 9$ .
So, there are 9 years between 2013 and 2022.

STEP 4

Our initial salary in 2013 is $\$65,000$ .
The inflation rate is $\$4\%$ per year, which we can write as $0.04$ .
We want to find the equivalent salary in 2022, after 9 years of inflation.

STEP 5

The formula for calculating the future value $FV$ of an amount, given the present value $PV$ , the rate of inflation $r$ , and the number of years $n$ is: $FV = PV \cdot (1 + r)^n$ This formula captures the compounding effect of inflation over the years.
Each year, the salary needs to increase by a factor of $(1 + r)$ to keep up with inflation.

STEP 6

Let's plug in our values: $PV = \$65,000$ , $r = 0.04$ , and $n = 9$ . $FV = \$65,000 \cdot (1 + 0.04)^9$

STEP 7

First, let's calculate $(1 + 0.04)$ , which is $1.04$ .
So, the formula becomes: $FV = \$65,000 \cdot (1.04)^9$

STEP 8

Now, let's calculate $(1.04)^9$ .
This is approximately $1.4115816$ .
So, the formula becomes: $FV = \$65,000 \cdot 1.4115816$

STEP 9

Finally, let's multiply $\$65,000$ by $1.4115816$ to get the final result: $FV \approx \$91,752.80$

STEP 10

To keep up with a $\$4\%$ annual inflation rate, a salary of $\$65,000$ in 2013 would need to be approximately $\$91,752.80$ in 2022.

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QuestionSuppose your salary in 2013 is $\$ 65,000$ . If the annual inflation rate is $4 \%$ , what salary do you need to make in 2022 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary. Formulas

Studdy Solution

STEP 1

What is this asking? How much money do we need to make in 2022 to have the same buying power as $\$65,000$ in 2013, given a $\$4\%$ yearly inflation? Watch out! Don't forget that salaries grow exponentially with inflation, not linearly!

STEP 2

1. Calculate the number of years.
2. Calculate the equivalent salary.

STEP 3

Let's figure out how many years have passed between 2013 and 2022.
It's as simple as subtracting the earlier year from the later year: $2022 - 2013 = 9$ .
So, there are 9 years between 2013 and 2022.

STEP 4

Our initial salary in 2013 is $\$65,000$ .
The inflation rate is $\$4\%$ per year, which we can write as $0.04$ .
We want to find the equivalent salary in 2022, after 9 years of inflation.

STEP 5

STEP 6

Let's plug in our values: $PV = \$65,000$ , $r = 0.04$ , and $n = 9$ . $FV = \$65,000 \cdot (1 + 0.04)^9$

STEP 7

First, let's calculate $(1 + 0.04)$ , which is $1.04$ .
So, the formula becomes: $FV = \$65,000 \cdot (1.04)^9$

STEP 8

Now, let's calculate $(1.04)^9$ .
This is approximately $1.4115816$ .
So, the formula becomes: $FV = \$65,000 \cdot 1.4115816$

STEP 9

Finally, let's multiply $\$65,000$ by $1.4115816$ to get the final result: $FV \approx \$91,752.80$

STEP 10

To keep up with a $\$4\%$ annual inflation rate, a salary of $\$65,000$ in 2013 would need to be approximately $\$91,752.80$ in 2022.

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QuestionSuppose your salary in 2013 is $65,000\$ 65,000$65,000. If the annual inflation rate is 4%4 \%4%, what salary do you need to make in 2022 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary. Formulas

Studdy Solution

STEP 1

What is this asking? How much money do we need to make in 2022 to have the same buying power as $65,000\$65,000$65,000 in 2013, given a $4%\$4\%$4% yearly inflation? Watch out! Don't forget that salaries grow exponentially with inflation, not linearly!

STEP 2

1. Calculate the number of years.2. Calculate the equivalent salary.

STEP 3

Let's **figure out** how many years have passed between 2013 and 2022.It's as simple as subtracting the earlier year from the later year: 2022−2013=92022 - 2013 = 92022−2013=9.So, there are **9 years** between 2013 and 2022.

STEP 4

Our **initial salary** in 2013 is $65,000\$65,000$65,000.The **inflation rate** is $4%\$4\%$4% per year, which we can write as 0.040.040.04.We want to find the equivalent salary in 2022, after **9 years** of inflation.

STEP 5

STEP 6

Let's **plug in** our values: PV=$65,000PV = \$65,000PV=$65,000, r=0.04r = 0.04r=0.04, and n=9n = 9n=9. FV=$65,000⋅(1+0.04)9FV = \$65,000 \cdot (1 + 0.04)^9FV=$65,000⋅(1+0.04)9

STEP 7

First, let's calculate (1+0.04)(1 + 0.04)(1+0.04), which is 1.041.041.04.So, the formula becomes: FV=$65,000⋅(1.04)9FV = \$65,000 \cdot (1.04)^9FV=$65,000⋅(1.04)9

STEP 8

Now, let's calculate (1.04)9(1.04)^9(1.04)9.This is approximately 1.41158161.41158161.4115816.So, the formula becomes: FV=$65,000⋅1.4115816FV = \$65,000 \cdot 1.4115816FV=$65,000⋅1.4115816

STEP 9

Finally, let's multiply $65,000\$65,000$65,000 by 1.41158161.41158161.4115816 to get the **final result**: FV≈$91,752.80FV \approx \$91,752.80FV≈$91,752.80

STEP 10

To keep up with a $4%\$4\%$4% annual inflation rate, a salary of $65,000\$65,000$65,000 in 2013 would need to be approximately $91,752.80\$91,752.80$91,752.80 in 2022.

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Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionSuppose your salary in 2013 is $\$ 65,000$ . If the annual inflation rate is $4 \%$ , what salary do you need to make in 2022 in order for it to keep up with inflation? Round your answer to the nearest cent, if necessary. Formulas

What is this asking? How much money do we need to make in 2022 to have the same buying power as $\$65,000$ in 2013, given a $\$4\%$ yearly inflation? Watch out! Don't forget that salaries grow exponentially with inflation, not linearly!

1. Calculate the number of years.
2. Calculate the equivalent salary.

Let's figure out how many years have passed between 2013 and 2022.
It's as simple as subtracting the earlier year from the later year: $2022 - 2013 = 9$ .
So, there are 9 years between 2013 and 2022.

Our initial salary in 2013 is $\$65,000$ .
The inflation rate is $\$4\%$ per year, which we can write as $0.04$ .
We want to find the equivalent salary in 2022, after 9 years of inflation.

Let's plug in our values: $PV = \$65,000$ , $r = 0.04$ , and $n = 9$ . $FV = \$65,000 \cdot (1 + 0.04)^9$

First, let's calculate $(1 + 0.04)$ , which is $1.04$ .
So, the formula becomes: $FV = \$65,000 \cdot (1.04)^9$

Now, let's calculate $(1.04)^9$ .
This is approximately $1.4115816$ .
So, the formula becomes: $FV = \$65,000 \cdot 1.4115816$

Finally, let's multiply $\$65,000$ by $1.4115816$ to get the final result: $FV \approx \$91,752.80$

To keep up with a $\$4\%$ annual inflation rate, a salary of $\$65,000$ in 2013 would need to be approximately $\$91,752.80$ in 2022.