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Future values of cash flows

investment does not meet

opportunity elsewhere.

The connection between fu

rate. The discount rate det

discounts the future value t

current period.

If the discount rate were 10

However, if the rate of retu

one would not pay more th

The other factors effecting

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are discounted because the investor demand a certain rate of return. If the

or exceed the investors expectations, he/she will look for a better

ture value of investment and present value of investment is the discount

rmine the discount factor, which when multiplied with the future value,

o the present value. This depends on the price one is willing to pay in the

% on a cash flow of 110 after 1 year, then the price would be 100.

rn required is 11%, then the price one is willing to pay changes. In this case,

an 99.1 for a cash flow of 110 after one year.

the discount rate is the inflationand risk.

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PROB 2

A

CD 18000

Future value for 8.4% 19,512.00

B

Future value for 3.2% 18,576.00 Analysis: If the level

Future value for 16.8% 21,024.00 If the level

C

The First National Bank of San Francisco offers CDs with an 8.4 percent nominal (stated)

interest rate but compounded semiannually.

Future value 19,543.75

As we can see that theEffective rate of interest 8.58% and the future value at

no difference

Future value using the effective 19,543.75

rate of interest

D

Pacific Trust offers 8.4 percent annual interest CDs with quarterly compounding


Bay State Savings and Loan offers the same rate with daily compounding


E

Bay State Savings and Loan offers the same rate with daily compounding


nominal rate the First National Bank have to offer to make its semiannual

compounding CD competitive with Bay State Savings and Loans daily compounding

CDFuture value 19,577.13

Present value 18,000

Required rate when compounded

semi annually 0.08577888 8.578%

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18576.00

of interest increases, the future value increases

of interest decreases, the future value decreases

future value compounded semi annually at 8.4%8.58%, which is the effective rate of interest have

There is a direct relation that exist between frequency of compounding

and future value

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PROB 4

Future value 35,000

Period 6 years

A

Present value -21,572.10

B

If 18000 is invested

To get 35000 as future value,

Rate of interest 11.72%

C

If only $18,000 is invested,stated rate the First National Bank must offer on its

semiannual compounding CD to accumulate the required funds


Effective annual rate of interest 11.72%

Pacific Trust


Effective annual rate of interest 11.72%

Bay State Savings and Loan.

Rate of interest 0.03037%Effective annual rate of interest 11.72%

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PROB 5

A

Annuity regular

B 8.40%

0 FV

1 3000 4,490.22

2 3000 4,142.27

3 3000 3,821.28

4 3000 3,525.17

5 3000 3,252.00

6 3000 3,000.00

Future value of the annuity 22,230.94

C semi annually8.40% Effective rate of interest 8.58%

1 3000 4,526.87

2 3000 4,169.30

3 3000 3,839.97

4 3000 3,536.65

5 3000 3,257.29

6 3000 3,000.00

Future vlue of annuity invested 22,330.08

with first national bank, compounded 22,330.08

semi annually

QUARTERLY

Effective rate of interest 8.67%

Future value of annuity compounded quarterly 22,381.93

Daily


Future value of annuity compounded Daily 22,434.79

D

Future value 35000

Interest rate 8.40%

Period 6 years

Equal installments -4,723.15

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The client is now paying 3000. Therefore the clients have to pay 1723 more to acquir

E

Future value 22230.940

Present value -13,701.94

F Period compuonding

0 FV

1 1500 2,457.56

2 1500 2,358.50

3 1500 2,263.44

4 1500 2,172.20

5 1500 2,084.65

6 1500 2,000.627 1500 1,919.98

8 1500 1,842.59

9 1500 1,768.33

10 1500 1,697.05

11 1500 1,628.65

12 1500 1,563.00

23,756.57

23,756.57


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Directly calculated using effective rate of interest

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35000 at the end of sixth year

Semi annual Compounding Quarterly compounding

0 FV 0 FV

1 1500 4,026.40 1 1500 4,067.49

2 1500 3,708.35 2 1500 3,743.04

3 1500 3,415.43 3 1500 3,444.46

4 1500 3,145.65 4 1500 3,169.70

5 1500 2,897.18 5 1500 2,916.86

6 1500 2,668.33 6 1500 2,684.187 1500 2,457.56 7 1500 2,470.07

8 1500 2,263.44 8 1500 2,273.03

9 1500 2,084.65 9 1500 2,091.72

10 1500 1,919.98 10 1500 1,924.86

11 1500 1,768.33 11 1500 1,771.32

12 1500 1,628.65 12 1500 1,630.02

31,983.93 32,186.76

31,983.93 32,186.76

Effective rate of interest 8.58% Effective rate of interest 8.67%

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12

11

10

9

8

76

5

4

3

2

1

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PROB 6

A

Annuity Due

B 8.40%

0 FV1 3000 4,867.40

2 3000 4,490.22

3 3000 4,142.27

4 3000 3,821.28

5 3000 3,525.17

6 3000 3,252.00

Future value of the annuity 24,098.34

C semi annually

8.40% Effective rate of interest 8.58%

1 3000 4,915.12

2 3000 4,526.87

3 3000 4,169.30

4 3000 3,839.97

5 3000 3,536.65

6 3000 3,257.29

Future vlue of annuity invested 24,245.20

with first national bank, compounded 24,245.20 Directly cal

semi annually

QUARTERLY


Future value of annuity compounded quarterly 24,322.06

Daily


Future value of annuity compounded Daily 24,400.49

D

Future value 35000

Interest rate 8.40%

Period 6 years

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Equal installments -4,357.15

The client is now paying 3000. Therefore the clients have to pay 1357 more to acquire 35

F Yearly compuonding Semi annual Compoun

0 FV 0

1 1500 2,457.56 1 1500

2 1500 2,358.50 2 1500

3 1500 2,263.44 3 1500

4 1500 2,172.20 4 1500

5 1500 2,084.65 5 1500

6 1500 2,000.62 6 1500

7 1500 1,919.98 7 1500

8 1500 1,842.59 8 1500

9 1500 1,768.33 9 1500

10 1500 1,697.05 10 1500

11 1500 1,628.65 11 1500

12 1500 1,563.00 12 1500

23,756.57

23,756.57

Effective rate of interest 8.40% Effective rate of intere

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culated using effective rate of interest

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000 at the end of sixth year

ding Quarterly compounding

FV 0 FV

4,026.40 1 1500 4,067.49

3,708.35 2 1500 3,743.04

3,415.43 3 1500 3,444.46

3,145.65 4 1500 3,169.70

2,897.18 5 1500 2,916.86

2,668.33 6 1500 2,684.18

2,457.56 7 1500 2,470.07

2,263.44 8 1500 2,273.03

2,084.65 9 1500 2,091.72

1,919.98 10 1500 1,924.86

1,768.33 11 1500 1,771.32

1,628.65 12 1500 1,630.02

31,983.93 32,186.76

31,983.93 32,186.76

st 8.58% Effective rate of interest 8.67%

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6

5

4

3

2

1

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PROB 7

A

8.40%

End of Year Payment A Payment B

0 15000 3000

1 0 3000

2 0 3000

3 0 3000

4 0 3000

5 0 3000

6 0 3000

Value of the payments -24,336.99 24,098.34

3000

27,098.34

B

End of Year Payment A Payment B

0 15000 3000

1 0 3000

2 0 30003 0 3000

4 0 3000

5 0 3000

6 0 3000

Value of the payments -24,336.99 24,098.34

3000

27,098.34

Future value 35000

present alue -21,572.10 -7,870.15

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Payment C Future values of payment C

1000 1,622.47

1500 2,245.11 6

2000 2,761.51 5

0 0.00 4

3500 4,112.70 3

4500 4,878.00 2

5500 5,500.00 1

21,119.79

Payment C Future values of payment C

1000 1,622.47

1500 2,245.11 6

2000 2,761.51 50 0.00 4

3500 4,112.70 3

4500 4,878.00 2

5500 5,500.00 1

21,119.79

19,497.32

-9,555.01 15,502.68

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PROB 8

A Effective annual rate 8.76%

B Present value 18000


C 0

1 3000 -4,565.88

2 3000 -4,198.02

3 3000 -3,859.79

4 3000 -3,548.81

5 3000 -3,262.89

6 3000 -3,000.00

-22,435.39

The interest for each annuity decreases as the compounding periods decreases for subs

therefore the total future value for annuities is less than that of the future value of the

D 0

1 3000 -4,965.99

2 3000 -4,565.88 Here we could observe the difference t

3 3000 -4,198.02 For the first annuity, we calculate the F

4 3000 -3,859.79 This is mainly because the payments a

5 3000 -3,548.81

6 3000 -3,262.89 -24,401.37

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equent annuities

ulk amount

o be 1965.99 when the paayments are made at the beginning of the period.

V at effective rate of 8.76% for 6 periods unlike the previous case where we took only five periods.

e made at the beginning of the year and an extra compounding period is added.

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6

5

4

3

2

1

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PROB 9

opening principal interest instalment principal repaid

yr1 35000 3570 11,089.32 7,519.32

yr2 27,480.68 2,803.03 11,089.32 8,286.29

yr3 19,194.39 1,957.83 11,089.32 9,131.49

yr4 10,062.90 1,026.42 11,089.32 10,062.90

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closing principal

27,480.68

19,194.39

10,062.90

0.00

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PROB 10

13500 10.2% monthly compunding

TIMELINE

0 1 2 3 4 5 6 7

13500 13500

the value of all the loan at the end of

year 9

values for e

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8 9 10 11 12 13 14 15 16

repayment starts

13500 13500 2292.55 2292.55 2292.55 2292.55 2292.55 2292.55 2292.55

FV

-20,266.42

-18,309.07

-16,540.76

-14,943.23 From amortization template

-70,059.48

ENTER VALUES

Loan amount

Annual interest rate

Loan period in years

Number of payments p

Start date of loan

quate quarterly installments for each loan's future value

-20,266.42 663.18 663.18 663.18 663.18 663.18 663.18 663.18

-18,309.07 599.13 599.13 599.13 599.13 599.13 599.13 599.13

-16,540.76 541.26 541.26 541.26 541.26 541.26 541.26 541.26

-14,943.23 488.99 488.99 488.99 488.99 488.99 488.99 488.99

2292.56 2292.56 2292.56 2292.56 2292.56 2292.56 2292.56

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17 18 19 20 21 22 23 24 25

2292.55 2292.55 2292.55 2292.55 2292.55 2292.55 2292.55 2292.55 2292.55

LOAN SUMMARY

$70,059.23 Scheduled payment $2,292.55

10.20% Scheduled number of p 60

15 Actual number of pay 60

4 Total early payments $17,300.00

Total interest $248,196.12

663.18 663.18 663.18 663.18 663.18 663.18 663.18 663.18 663.18

599.13 599.13 599.13 599.13 599.13 599.13 599.13 599.13 599.13

541.26 541.26 541.26 541.26 541.26 541.26 541.26 541.26 541.26

488.99 488.99 488.99 488.99 488.99 488.99 488.99 488.99 488.99

2292.56 2292.56 2292.56 2292.56 2292.56 2292.56 2292.56 2292.56 2292.56

SEC A- GRP 9

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