6. Answer the following questions:

a)

Suppose you are receive $47,000 per year, but get a $1000 raise every k = 3 years.

That is, you are paid $47,000 in years 1, 2, ..., k, and paid ($47,000 + $1,000) in years k+1, k+2, ..., 2k, and paid ($47,000+$2,000) in years 2k+1, 2k+2, ..., 3k, and so on into perpetuity. Given an interest rate 2.1%, what is the present value of these cash flows? (to nearest $0.01) (Hint: I suggest you work out a formula rather than just calculating numerically. Can you convert this question to the PV of an annuity of length 3 years? Also see HW 2, question 3.)

b) Suppose you invest $5,000 today, and you will receive $6,000 ten years from today, and you will also receive $5,000 twenty years from today. What is your internal rate of return? (To nearest 0.01%, and e.g. for 5.02%, put in 5.02 not 0.0502).

c) Given a bond with coupon 5% and maturity 2 years, if it has a price of 95, what is it's yield? (Nearest 0.01%, but input e.g. 5.02 for 5.02%, not 0.0502).

d) Given an annuity which pay $8,000 per year for 7 years, and an interest rate of 9.7%, what is its duration? (to the nearest 0.01 years)

e) Suppose you receive a payment of $4,000 one year from now, but in year 2 the payment will have grown by 2.7% to $4,000 times (1 + 2.7/100), and in year 3 it will have grown by another 2.7%, so that you receive $4,000 times (1 + 2.7/100)^2, and so on into perpetuity. Note that this is compound growth, not linear.

Given an interest rate 3.7%, what is the duration of these cash flows? (nearest 0.01 years)

The answer to these problems are a) 2,978,300.03 b) 5.85 c) 7.75 d) 3.63 e) 103.70.

I want the equations to get these answers.

Thank you!

Thank you!