Question

1. You are pleased to see that you have been given a 5.95% raise this year. However, you read on the Wall Street Journal Web site that inflation over the past year has been 1.81%. How much better off are you in terms of real purchasing power? (Note: not to around any intermediate steps less than six decimal places)
Your real purchasing power is ________% (round to two decimal)

2. If the rate of inflation is 5.8%, what nominal interest rate is necessary for you to earn a 3.8% real interest rate on your investment? (Note: not to around any intermediate steps less than six decimal places)
The nominal interest rate is ______ % (round to two decimal)

3. You are thinking about investing $4,816 in your friend's landscaping business. Even though you know the investment is risky and you can't be sure, you expect your investment to be worth $5,726 next year. You notice that the rate for one-year Treasury bills is 1%. However, you feel that other investments of equal risk to your frined's landscape business offer an expected return of 10% for the year. What should you do?
a. The present value of the return is $ __________
b. You should ____________

Please Explain to me step by step with answer

Thank you

Answer 1

1.

Real purchasing power = (1 + 5.95%) / (1 + 1.81%) - 1

= 1.0407 - 1

= 4.07%

Real purchasing power is 4.07%

2.

Nominal rate of return = (1 + 5.80%) × (1 + 3.80%) - 1

= 1.0982 - 1

= 9.82%

Nominal rate of return is 9.82%.

3.

Expected rate of return = ($5,726 / $4,816) - 1

= 1.1890 - 1

= 18.90%

Expected rate of return is 18.90%.

Other investments of equal risk to your frined's landscape business offer an expected return of 10% and expected return from portfolio is 18.90%. Since, expected return is higher than required return, so he should make investment.

Present value of return = $5,726 / (1 + 10%)

= $5,205,45.

Present value of return is more than initial investment, so he should invest in project.