Question

1. Last year, the CPI Index was 102.43. Now (one year later), the index is 110.24.

Calculate the inflation rate over this period.

Enter your answer in decimals (not percent) and round to 4 decimal places, for example 0.1234.

2. Last year, the CPI Index was 205.49. Now (one year later), the index is 214.87.

Over the past year, you earned 7.6% on your deposits at the bank.

Calculate your real rate of return over the year.

Enter your answer in decimals (not percent) and round to 4 decimal places, for example 0.1234.

3.

Company A and Company B recently sold bonds to investors.

You notice that investors require a return of 4.55% to invest in the bonds of Company A, and they require a return of 8.75% to invest in the bonds of Company B.

Which of the following options would be the most likely explanation for the extra return investors require from Company B?

Group of answer choices

Company B has more default risk than Company A

Company A has more default risk than Company B

Investors are not sure how much liquidity risk there is for Company B

Investors expect more profits from Company B

4.

What is the present value of a 8-year annuity that will pay you $3,000 per year if interest rates are 10%?

Round your answer to 2 decimal places, for example 100.12.

Answer 1

1) Inflation rate over the period = Current year CPI - Last year CPI / Last year CPI

= 110.24 - 102.43 / 102.43

= 7.81/102.43

= 0.0762

Thus ans : Inflation rate = 0.0762

2) Let us first calculate inflation rate

Inflation rate over the period = Current year CPI - Last year CPI / Last year CPI

= 214.87 - 205.49 / 205.49

= 9.38 / 205.49

= 0.0456

i.e 4.56%

Real rate of return = (1+nominal rate of return)/(1+inflation rate) - 1

= (1+7.6%)/(1+4.56%) - 1

= 1.076/1.0456 - 1

= 1.02907 - 1

= 0.0291

Thus ans) Real rate of return = 0.0291

3) Ans) Company B has more default risk than Company A

Required rate for bond is calculated by adding default risk premium of bond to risk free rate of interest, higher the default risk higher will be required return

4) Here formula of present value of annuity can be used

PV(annuity) = A[1-(1/(1+r)^n / r]

A = annuity = $3000

r = rate of interest = 10%

n = no of years = 8

Thus PV(annuity) = 3000[1-(1/(1+10%)^8) / 10%]

= 3000[1-(1/(1+0.1)^8 ) / 0.1]

= 3000[1-(1/1.1)^8 / 0.1]

= 3000[ 1 - 0.466507 / 0.1]

= 3000[0.53349/0.1]

= 3000 x 5.3349

= 16004.78 $

Thus ans) 16004.78$