# Present value and future value problems

23. Determine how much an investor would collect after 25 years if $100,000 is deposited and is compounded annually at 10%.

25. What is the future value of a $250 annuity at the end of the next 5 years if the annual compounding rate is 10%?

26. A zero coupon government bond can be converted to $25,000 at maturity 10 years from now. What is the value of this bond if the discount rate in the bond market is 9%?

27. You have borrowed $6,000 from the ABC Bank for a period of 4 years. The annual interest rate is 12%. Can you determine your annual repayment of the loan?

28. A share of preferred stock is usually viewed as a perpetuity. If the actual dividend of a preferred stock is $5 and the discount rate is 10%, what is the value of that preferred stock.

29. You need $30,000 to use for a down payment on a vacation home in 10 years. You can obtain a return of 8% in a particular investment vehicle and you would like to contribute to your vacation home fund each month. How much money would you have to put aside each month to achieve your objective?

31. What is rate must you obtain to be able to afford a $100,000 boat in 10 years if you are willing to put aside $1,000 each quarter and have $50,000 set aside today?

Using the information in problem 31, what amount would the investor collect if the this investment used daily compounding?

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#### Solution Preview

23. pv=-100,000

n=25

i =10

compute FV= 1,083,470.59

25. pmt=-250

n= 5

i = 10

compute fv= 1526.275

26. ...

#### Solution Summary

The solution discusses the present value and future value problems.

Compute the present value of this stream of income at a discount rate of 8%. Compare the present values of the income stream under the three discount rates.

Suppose you just inherited a gold mine. This gold mine is believed to have three years worth of gold deposit. Here is how much income this gold mine is projected to bring you each year for the next three years:

Year 1: $42,000,000

Year 2: $62,000,000

Year 3: $99,000,000

Compute the present value of this stream of income at a discount rate of 8%. Remember, you are calculating the present value for a whole stream of income, i.e. the total value of receiving all three payments (how much you would pay right now to receive these three payments in the future). Your answer should be one number - the present value for this oil well at a 8% discount rate but you have to show how you got to this number.

Now compute the present value of the income stream from the gold mine at a discount rate of 6%, and at a discount rate of 4%. Compare the present values of the income stream under the three discount rates.