- Compute the present value of $100 in
*t*years for the following combinations of discount rates and times:- r = 10 percent, t = 10 years

PV = FV * (1 + i)^{-n}

= 100(1.1)-10 = $38.55

- r = 10 percent, t = 20 years

= 100 (1.1)-20 = $14.86

- r = 5 percent, t = 10 years

= 100 (1.05)-10 = $61.35

- r = 5 percent, t = 20 years

= 100 (1.05)-20 = $37.69

- Would you prefer to receive $10,000 in one year or $20,000 in five years, if the interest rate is
- 0 percent?

PV = FV * (1 + i)^{-n}

^{ }PV(10,000) = 10,000 PV(20,000)= 20,000 Prefer $20,000

- 10 percent?

PV = 10,000 (1.1)-1 = $9091 PV = 20,000 (1.1)-5 = $12418 Prefer $20,000

- 20 percent?

PV= 10,000 (1.2)-1 = $8333 PV = 20,000 (1.2)-5 = $8038 Prefer 10,000

- Find the interest rate implied by the following:
- Present value = 100, future value = 171, years = 11

PV = FV * (1 + i)^{-n}

100 = 171 (1+r)-11

1+r = (100/171)^{-1/11}

1+r = 1.05 r = 1.05-1 = 0.05 = 5%

- Present value = 200, future value = 322.10, years = 5

200 = 322.10 (1+r)-5

1+r = (200/322.10)^{-1/5}

1+r = 1.1 r = 1.1 – 1 = 0.1 = 10%

- What is the present value of the following stream of cash flows: $200 in one year, $300 in two years and $400 in three years if the interest rate is 8%?

PV = C * (1-(1+i)^{-n} /i)

PV (200) = 200*(1-(1.08)-1/0.08) = $185.19

PV(300) = 300 * (1-(1.08)-2/0.08) = $534.98

PV(400) = 400 * (1-(1.08)-3/0.08) = $1030.84

- Suppose you have just celebrated your 19th birthday. A rich uncle has set up a trust fund for you that will pay you $150,000 when you turn 30. If the relevant discount rate is 9 percent, how much is this fund worth today?

PV = FV * (1 + i)^{-n}

PV = 150,000 * (1.09)-30 = $11,305.67

- Your parents will retire in 18 years. They currently have $250,000, and they think that they will need $1,000,000 at retirement. What interest rate must they earn to reach their goal (assuming they will not save any additional funds)?

PV = FV * (1 + i)^{-n}

250, 000 = 1000,000 (1 + r)-18

1 + r = (250,000/1,000,000)^{-1, 18}

r = 1.08 – 1 = 0.08 = 8%

- If you deposit your money today in an account that pays 6.5% annual interest, how long will it take to double your money?

PV = FV * (1 + i)^{-n}

1 = 2 (1.065)-n

log0.5 = -nlog1.065

-n = -11 n = 11 years.