Question

1. If your total income in 2020 is $40,000 and your income in 2021 is expected to be $45,000.
   1. What is your real income in 2021 if the inflation rate (price level) is 6%? (Present the equations you are using and your calculation.) (1 point)
   2. Ignoring inflation, what is the discounted present value of your two-year flow of nominal income if interest rate is 5%? (Present the equations you are using and your calculation.) (1 point)
   3. In a sentence answer why your answer in b) is less than the sum of $40,000 and $45000. (0.5 points)

This is a 3 part question not 3 different questions please answer all parts, thank you!

Answer 1

Part 1)

Income in 2020 = $40000

Income in 2021 ( expected ) = $45000

Inflation ( increase in price level ) = 6%

Real income = nominal income / (1 + rate of inflation ( in %) ) [ We divide it by increase in inflation since we can now afford to buy less amount of goods and service because of the increase in price levels. Therefore, in real terms our income decreases)

Real income in 2020 = 45000 / (1+0.06) = 45000/1.06

=> Real income in 2020 = $42,452.83

Part 2)

Interest rate = 5%

Discounted present value = Cash flow in year 1 / ( 1 + r )¹ + Cash flow in year 2 / ( 1 + r )² + ... Cash flow in year n / ( 1 + r )ⁿ

n = number of the year

r = rate of interest in percentage

If the income for the respective years is being received at the beginning of the year

Therefore, in the discounted value of cash flow for the question =

40,000 / ( 1 + 0.05)⁰ + 45000 / (1 + 0.05)¹

= $ 82,857.14

If the income for the respective years is being received at the end of the year

Therefore, in the discounted value of cash flow for the question =

40,000 / ( 1 + 0.05)¹ + 45000 / (1 + 0.05)²

= $ 78,911.56

Part 3)

The present value of the two year incomes would be less than the sum of 40000 and 45000 because of the time value of money. Money received at a later time period is worth less than money received right now.