Time Value of Money

Question 1

Formula of getting Real Interest

Answer 1

Nominal Interest Rate - Inflation Interest Rate

Question 2

2 kinds of Interest

Answer 2

1. Simple Interest
2. Compound Interest

Question 3

Formula of Getting Simple Interest (shortcut)

Answer 3

FV = PV (1+rt)

Question 4

Formula of getting Simple Interest (the original)

Answer 4

P x R x T

Question 5

What’s two kinds of Compound Interest

Answer 5

1. Annually Compound Interest
2. Semi-annual (2); Quarterly (4); Monthly (12) Compound Interest

Question 6

Formula of getting Annually Compound Interest

Answer 6

FV = PV (1+r)^t

Question 7

Formula of getting Semi-annual (2); Quarterly (4); Monthly (12) Compound Interest

Answer 7

FV = PV (1 + r/m)^m x t

Question 8

Is the value of a group of receiving payments at a certain date in future.

Answer 8

Annuities

Question 9

The higher the discount rate, the greater the annuity’s FV.

Answer 9

Annuities

Question 10

How much money will be required to produce a series of future payments.

Answer 10

Present Value of Annuity

Question 11

How much money a series of payments will be worth at a certain point in the future.

Answer 11

Future Value of Annuity

Question 12

Payments due made at the end of each agreed period.

Answer 12

Ordinary Annuity

Question 13

Payments due made at the beginning of each agreed period.

Answer 13

Annuity Due

Question 14

Formula of Getting Ordinary Annuity (Method 1)

Answer 14

FV = PV X [(1 + r)^t - 1] / r

Question 15

Formula of getting Annuity Due (Method 1)

Answer 15

FV = [(1 + r)^t - 1] / r x (1 + r)

Question 16

Formula of getting Ordinary Annuity (Method 2)

Answer 16

FV = PV x FVIFA (table 2)

Question 17

Formula of getting Annuity Due (Method 2)

Answer 17

FV = PV x FVIFA (table 2) x (1 + r)

Question 18

Formula of getting Present Value

Answer 18

PV = FV / (1+r)^t

Question 19

Scenario:

PV = 100,000 ; R = 5%; T = 3 years

Find the simple interest.

Answer 19

FV = 100,000 x (1+0.05x3)
= 115,000

Question 20

Scenario:

PV = 100,000 ; R = 5%; T = 3 years

Find the compound annual interest using (3 methods).

Answer 20

Method 1:
FV1 = 100,000 x (1 + 0.05 x 1) = 105,000
FV2 = 105,000 x (1 + 0.05 x 1) = 110, 250
FV3 = 110,250 x (1 + 0.05 x 1) = 115, 762.50

Method 2:
FV = 100,000 x (1 + 0.05)^3 =115,762.50

Method 3:
FV = 100,000 x 1.1576 = 115, 760

Question 21

Scenario:

PV = 250,000; R = 8%; T = 5 years

Find simple interest

Answer 21

FV = 250,000 x (1 + 0.08 x 5) = 350,000

Question 22

Scenario:

PV = 250,000; R = 6%; T = 5 years

Find compounded annually ( 2 methods)

Answer 22

Method 1:
FV = 250,000 x (1 + 0.06)^5 = 334, 556.39

Method 2:
FV = 250,000 x 1.3382 = 334, 550

Question 23

Scenario:

PV = 250,000; R = 5.5%; T = 5 years

Find compounded monthly interest

Answer 23

Method 1:
FV = 250,000 x ((1 + (0.055/12)^12x5 = 328, 925. 94

Question 24

Scenario:

PV = 1,000; R = 5%; T = 5 years

Find FV ordinary annuity (2 methods)

Answer 24

Method 1:
FV = 1,000 x ((1 + 0.05)^5 - 1) / 0.05 = 5,525.63

Method 2:
FV = 1,000 x 5.5256 = 5, 525.60

Question 25

Scenario:

PV = 1,000; R = 5%; T = 5 years

Find annuity due (2 methods)

Answer 25

Method 1:
FV = 1,000 x ((1 + 0.05)^5-1)/0.05 x (1+0.05) = 5,801.91

Method 2:
FV = 1,000 x 5.5256 x (1+0.05) = 5,801.88

Question 26

Scenario:

PV = 125,000; R = 8%; T = 5 years

Find FV ordinary annuity (2 methods)

Answer 26

Method 1:
FV = 125,000 x ((1 + 0.08)^5 - 1 / 0.08 = 733, 325.12

Method 2:
FV = 125,000 x 5.8666 = 733, 325

Question 27

Scenario:

PV = 125,000; R = 8%; T = 5 years

Find FV of Annuity Due ( 2 methods)

Answer 27

Method 1:
FV = 125,000 x ((1 + 0.08)^5 - 1 / 0.08 X (1+0.08) = 791,991.13

Method 2:
FV = 125,000 x 5.8666 x (1+0.08) = 791,991

Question 28

Scenario:

PV = 100,000; R = 5%; T = 5 years

Find PV of cash flow ( 2 methods)

Answer 28

Method 1:
PV = 100,000/(1+0.05)^5 = 78,354.62

Method 2:
PV = 100,000 x 0.7835 = 78,350

Question 29

Scenario:

PV = 200,000; R = 4%; T = 3 years

Find PV of cash flow ( 2 methods)

Answer 29

Method 1:
PV = 200,000/(1+0.04)^3 = 177, 799.27

Method 2:
PV = 200,000 x 0.8890 = 177, 800

Question 30

Scenario:

PV = 100,000; R = 5%; T = 3 years

Find quarterly compound

Answer 30

FV = 100,000 x (1+ 0.05/4)^4x3 = 116,075.45

Question 31

Scenario:

PV = 100,000; R = 3%; T= 1 year

Find Present Value

Answer 31

PV = 100,000 / (1 + 0.03)^1
= 97,087

Question 32

Scenario:

PV = 100,000; R = 3%; T = 3 years

Find Present Value

Answer 32

PV = 100,000 / (1+0.03)^3
= 91,514.17

Question 33

Senario:

PV = 2,000,000; R = 5%; T = 10 years

Find Present Value

Answer 33

PV = 2,000,000 / (1+0.05)^10
= 1,227,826.51

Question 34

Scenario:

Year 1 = 100,000
Year 2 = 200,000
Year 3 = 250,000

R = 3%

Find Present Value

Answer 34

Year 1 = 100,000 x 0.9709 = 97,090
Year 2 = 200,000 x 0.9426 = 188,520
Year 3 = 250,000 x 0.9151 = 228,775

Total PV = 514,385

Question 35

Scenario:

PV = 220,000; R= 3%; T = (for) 4 years

Find Present Value

Answer 35

PV = 220,000 x 3.7171
= 817, 762

Question 36

Scenario:

Year 0 = 30M (initial Investment)

Projected Cash inflows:
Year 1 = 2M
Year 2 = 3M
Year 3 = 3.5 M
Year 4-10 = 4M (7 years)
Year 11-20 = 3M

Interest rate: 12%

a.) Find the total PVCI
b.) Find NPV

Answer 36

Year 1 = 2M x 0.8929 =
Year 2 = 3M x 0.7972 =
Year 3 = 3.5 M x 0.7118 =

Question 37

Scenario:

FV = 500,000; R = 8%; T = 3 years

Find the Present Value

Answer 37

notebook

Question 38

Scenario:

Year 1 = 200,000
Year 2 = 220,000
Year 3 = 300,000
Year 4 = 300,000
Year 5 = 300,000

Interest = 10%

Answer 38

notebook

Question 39

Find the PV of 350,000 at the end of Year 6 using a discount rate of 5%.

Answer 39

Paper

Question 40

Find the total PV of Cash inflow of the ff:

Year 1-5 = 300,000
Year 6 = 500,000
Year 7 = 600,000
Year 8 = 800,000

R = 10%

Answer 40

paper