Assume payments of $2,000, $5,000, and $3,000 are received at t = 3, 4, and 5, respectively. What five equal payments occurring at the end of t = 1, 2, 3, 4, and 5, respectively, are equivalent if i = 10% compounded per period? 

3. Given the cash flow profiles shown below, determine the value of X so that the two cash flow profiles are equivalent at a 10% interest rate. Use gradient series factor wherever appropriate.

End of Year

Cash Flow of (A)

Cash Flow of (B)

1

-$12,000

-$10,000

2

1,000

7,000

3

3,000

6,000 + 0.5x

4

5,000

5,000 + 1.0x

5

7,000

4,000 + 1.5x

6

9,000

4. If the interest on a certain sum for three months is $63.87 at 5% simple interest, what would it be at 6%?

5. Tuition costs are expected to increase at a rate of 8% per year. The first year's tuition is due one year from now and will be $2,000. A fund is to be set up today to cover tuition costs for 4 years in an account that will earn interest rate (i). How large must the fund be if:

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a) i = 5%

b) i = 8%

c) i = 10%

6. Given the cash flow profiles shown below, determine the value of X such that the two cash flow profiles are equivalent at 8% compounded annually.

End of year

CF(A)

CF(B)

1

-$12,000

-$X

2

1,000

7,000

3

4,000

9,000

4

6,000

10,000

5

7,000

10,000

6

5,000

7,000

7. How long will it take $800 to yield $72 in simple interest at 4%?

8. A construction company is planning to buy a warehouse for $190,000. They intend to keep the warehouse for 6 years and expect the annual upkeep and taxes to amount to $900 per year. Without any major repairs, the warehouse should have a resale price of $160,000. What is the equivalent annual cost of owning the warehouse if the company's acceptable interest rate is 6%?

9. Maintenance records of an excavation machine indicate that the first-year maintenance cost of $800 increases by $300 per year over the 10-year replacement period of the machine. If the maintenance cost is considered to occur at the end of the year and the firm's interest rate is 12%:

a) What equal annual payment could the firm make to a service organization to carry out the maintenance for 20 machines?

b) How much additional could be paid for a new type of machine with the same service life that required no maintenance during its life?

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10. Traffic flow over a new bridge is expected to be one million vehicles the first year it is in use. If the average traffic rate is expected to increase by 5% per year:

a) Determine the expected number of vehicles using the bridge in the twentieth year of service.

b) Assuming that a toll of $1 per vehicle is charged for use of the bridge, determine the present worth of all projected toll collections using an interest rate of 8%.