Assume your uncle recorded his salary history during a 40-year career and found that it had increased 10-fold.If inflation averaged 4% annually during the period,how would you describe his purchasing power,on average?

Question

Quizplus · Accepted Answer

If the salary increased by 10-fold, it means the salary at the end of the 40-year career was 10 times the starting salary. We can represent this as (1 + 9)S, where S is the starting salary.

Now, with an average annual inflation rate of 4%, the purchasing power of money decreases by 4% each year. So, after 40 years, the purchasing power of money will have decreased by (1 + 0.04)^40 or approximately 3.24 times.

Therefore, the uncle's salary increased by 10 times, but the purchasing power of money decreased by 3.24 times. So, the real increase in salary after adjusting for inflation is approximately 10/3.24 or 3.08 times.

Now, to find the average annual increase in purchasing power, we can use the following formula:

Average annual increase in purchasing power = (1 + real increase in salary)^(1/40) - 1

= (1 + 3.08)^(1/40) - 1

= 0.038 or approximately 3.8%

Therefore, the uncle "beat" inflation by slightly below 2% annually, as the real increase in purchasing power is 3.08 times, while the average annual increase in purchasing power is 3.8%.

Assume Your Uncle Recorded His Salary History During a 40-Year