financial math worksheet: wages and inflation\nthis worksheet will help you understand the impact of…

financial math worksheet: wages and inflation\nthis worksheet will help you understand the impact of inflation on wages and the difference between nominal and real wage growth.\npart a: key definitions\n1. nominal wage growth: the increase in wages without adjusting for inflation (the wage you see on your paycheck).\n2. real wage growth: the increase in wages after adjusting for inflation (your actual purchasing power).\npart b: practice problems\n1. alex earns $15 per hour in 2020. by 2025, alexs wage increases to $18 per hour. if the average annual inflation rate over this period is 3%, calculate alexs nominal wage growth percentage and real wage growth percentage.\n2. jordans weekly wage in 2018 was $500. in 2025, jordans weekly wage is $650. during this time, prices increased by 20%. calculate jordans nominal wage growth percentage and real wage growth percentage.\n3. mia earned $40,000 in 2022 and received a raise to $44,000 in 2023. if inflation during this period was 6%, what is mias nominal and real wage growth?\n4. define in your own words: why is it important to look at real wage growth instead of only nominal wage growth?\npart c: wage growth table\n| name | initial wage | final wage | inflation (%) | nominal growth (%) | real growth (%) |\n| ---- | ---- | ---- | ---- | ---- | ---- |\n| alex | $15/hr | $18/hr | 3% | | |\n| jordan | $500/wk | $650/wk | 20% | | |\n| mia | $40,000/yr | $44,000/yr | 6% | | |

financial math worksheet: wages and inflation\nthis worksheet will help you understand the impact of inflation on wages and the difference between nominal and real wage growth.\npart a: key definitions\n1. nominal wage growth: the increase in wages without adjusting for inflation (the wage you see on your paycheck).\n2. real wage growth: the increase in wages after adjusting for inflation (your actual purchasing power).\npart b: practice problems\n1. alex earns $15 per hour in 2020. by 2025, alexs wage increases to $18 per hour. if the average annual inflation rate over this period is 3%, calculate alexs nominal wage growth percentage and real wage growth percentage.\n2. jordans weekly wage in 2018 was $500. in 2025, jordans weekly wage is $650. during this time, prices increased by 20%. calculate jordans nominal wage growth percentage and real wage growth percentage.\n3. mia earned $40,000 in 2022 and received a raise to $44,000 in 2023. if inflation during this period was 6%, what is mias nominal and real wage growth?\n4. define in your own words: why is it important to look at real wage growth instead of only nominal wage growth?\npart c: wage growth table\n| name | initial wage | final wage | inflation (%) | nominal growth (%) | real growth (%) |\n| ---- | ---- | ---- | ---- | ---- | ---- |\n| alex | $15/hr | $18/hr | 3% | | |\n| jordan | $500/wk | $650/wk | 20% | | |\n| mia | $40,000/yr | $44,000/yr | 6% | | |

Answer

Explanation:

Step1: Calculate nominal wage growth percentage formula

The formula for nominal wage growth percentage is $\frac{\text{Final Wage}-\text{Initial Wage}}{\text{Initial Wage}}\times100%$.

Step2: Calculate real wage growth percentage formula

The formula for real wage growth is based on the Fisher - equation concept. First, find the price index factor. If inflation rate is $i$, the price index factor is $(1 + i)$. Then real wage growth percentage = $\left(\frac{\text{Final Wage}/(1 + i)-\text{Initial Wage}}{\text{Initial Wage}}\right)\times100%$.

Problem 1: Alex

Nominal wage growth percentage

Step1: Apply nominal wage growth formula

$\frac{18 - 15}{15}\times100%=\frac{3}{15}\times100% = 20%$

Real wage growth percentage

Step1: Calculate price - index factor

The inflation rate $i = 0.03$, so the price - index factor is $1+0.03=1.03$.

Step2: Apply real wage growth formula

$\left(\frac{18/1.03 - 15}{15}\right)\times100%=\left(\frac{17.4757 - 15}{15}\right)\times100%=\left(\frac{2.4757}{15}\right)\times100%\approx16.5%$

Problem 2: Jordan

Nominal wage growth percentage

Step1: Apply nominal wage growth formula

$\frac{650 - 500}{500}\times100%=\frac{150}{500}\times100% = 30%$

Real wage growth percentage

Step1: Calculate price - index factor

The inflation rate $i = 0.2$, so the price - index factor is $1 + 0.2=1.2$.

Step2: Apply real wage growth formula

$\left(\frac{650/1.2-500}{500}\right)\times100%=\left(\frac{541.67 - 500}{500}\right)\times100%=\left(\frac{41.67}{500}\right)\times100%\approx8.33%$

Problem 3: Mia

Nominal wage growth percentage

Step1: Apply nominal wage growth formula

$\frac{44000 - 40000}{40000}\times100%=\frac{4000}{40000}\times100% = 10%$

Real wage growth percentage

Step1: Calculate price - index factor

The inflation rate $i = 0.06$, so the price - index factor is $1+0.06 = 1.06$.

Step2: Apply real wage growth formula

$\left(\frac{44000/1.06-40000}{40000}\right)\times100%=\left(\frac{41509.43 - 40000}{40000}\right)\times100%=\left(\frac{1509.43}{40000}\right)\times100%\approx3.77%$

Problem 4:

Nominal wage growth only shows the increase in the amount of money received, but it doesn't account for the change in the value of money due to inflation. Real wage growth reflects the actual change in purchasing power. If nominal wage growth is high but inflation is even higher, the real wage may actually decrease, meaning workers can buy fewer goods and services despite the increase in their paycheck amount. So, real wage growth gives a more accurate picture of the economic well - being of workers.

Answer:

Alex

Nominal wage growth percentage: $20%$ Real wage growth percentage: $\approx16.5%$

Jordan

Nominal wage growth percentage: $30%$ Real wage growth percentage: $\approx8.33%$

Mia

Nominal wage growth percentage: $10%$ Real wage growth percentage: $\approx3.77%$

Question 4

It is important to look at real wage growth instead of only nominal wage growth because real wage growth reflects actual change in purchasing power, while nominal wage growth does not account for inflation.