Arithmetic And Geometric Gradient

Gradient Series of Cash Flows

UNIFORM GRADIENT SERIES OF CASH FLOWS Arithmetic gradient series is a series of payments in which each payment is greater than or less than previous one by a constant amount GEOMETRIC SERIES OF CASH FLOWS Geometric gradient series is series of payments where annual payments increase or decrease over time, by a constant percentage.

1. Find the value of each of the following: a. (A/G, 14.5%,23) b. (P/G, 12%,10) c. (F/G,7.8%,21) 2. Compute for the present value 50

10 0

150

0 0

1

2

i= 10%

3

4

3. Compute the value of the amount of F 200 50 0

1

100

15 0

2

3

4

i= 10%

4. Compute the value of the amount of A 300 100

20 0

2

3

400

0 0

1

i= 10%

4

5

5. For the gradient series shown below, compute for the values of P and F and the value of A 500

0

1

45 0

2 i= 10%

400

3

35 0

4

300

5

25 0

6

6. Suppose a man receives an initial annual salary of $60,000, increasing at the rate of $5,000 a year. If money is worth 10%, determine his equivalent uniform salary for the period of 8 years.

7. Deposit are made to an account as indicated below which bears interest at the rate of 10% compounded annually. How much will there be in the account the end of the sixth year? End of year

Deposit

1

P0

2

500

3

1000

4

1500

5

2000

8. An increasing annual uniform series begins at the end of second year

and ends after

fifteenth year. What is the value of gradient G that makes the gradient series equivalent to a uniform flow of payments of Php 900 per year for seven years at 12% per year compounded annually?

Geometric Gradient The rate of increase is (1+r )

1. For the cash flow shown below, find the values of present and future if i = 12% per year 1000 1100

1210

0

r = 10% i= 12%

1331

1464.10

2. For the cash flow shown below, find the values of present and future if i = 12% per year 3000

0

1

2250

2

1687.50

3

1265.63 949.22

4

5

711.91

6

533.94

7

400.45 8

3. Annual maintenance cost for the machine are 1,500 this year and estimated to increase 10% each year every year. What is the present worth of the maintenance cost for 6 years if i= 8%

4.

Lovely a 3rd year student of Industrial Engineering Department in Adamson University with a age of 18 years old makes year end deposit of Php 500 for the first year, P 550 on the 2nd year, P 605 on the 3rd year and so on, increasing the next year’s deposit by 10% of the deposit by the preceding year until the end of tenth year. Desiree makes equal year end deposits of 700 each year for 10 years. If interest on both funds is 12% compounded annually, who will be able to save more at the end of 10 years?

5. On Domingo’s 23rd birthday you decide to invest $4,500 (10% of your annual salary) in a mutual fund earning 7% per year. You will continue to make annual deposits equal to 10% of your annual salary until you retire at age 62 (40 years after you started your job). You expect your salary to increase by an average of 4% each year during this time. How much money will you have accumulated in your mutual fund when you retire?