Finance questions

9. What is the present value of the following stream of cash flows if the appropriate discount rate is 5% per annum: $2,500 paid in 1 year; $3,500 paid in 3 years and $7,000 paid in 5 years?

10. You are considering the purchase of a security that costs $4,400 today. It offers an 11% return per year, compounded quarterly. If you purchase the security, you would receive payments of $1,000 in 1 year, $2,000 in 2 years, and $x in 4 years. How much must x be for you to receive the promised return?

11. You are attempting to determine how much money will be in your retirement account in 20 years. You will deposit $10,000 today and then again every other year until year 10 (e.g., t=2, 4, 6, 8, and 10). You will withdraw $5,000 every other year with the first withdrawal occurring at t=1 (e.g., t=1, 3, 5, 7, and 9). The account pays a 9% interest rate. How much money will be in the account in 20 years?

12. Suppose you are thinking about purchasing a machine that costs $100,000 and can produce $8,000 in after-tax cash flow per year. The risk associated with this product corresponds to a 12% discount rate. How many years must the machine last for you to break even on this investment?

13. You are considering an annuity that would pay you $6,000 every three years. The annuity would make 15 payments and the first payment would occur in 2 years (e.g., the payments would occur at t=2, 5, 8,). If the interest rate associated with this annuity is 7.5% per annum, what is the present value of this annuity?

14. You want to be able to withdraw $50,000 per year for 30 years once you retire with the first withdrawal taking place one year after retirement. You plan on retiring in 30 years and plan to make monthly deposits until that point. The first deposit will be made today and the final one will be made 30 years from today. While you work, you will invest your funds in a more aggressive investment strategy that offers you a 9% return p.a. However, when you retire, you will shift your funds to a safer investment strategy that only pays 3% p.a. How much must you deposit each month to fund your retirement account?

15. What is the present value of a perpetuity that pays you $200 every other year if the first payment is to be made in 3 years and the appropriate discount rate is 7% p.a.?