Time value of moneyPart 1

Time value of money

Obviously, 1,000,000 Taka today1,000,000 Taka today.

You already recognize that there is TIME VALUE TO MONEYTIME VALUE TO MONEY!!

Which would you prefer –

1,000,000 Taka today1,000,000 Taka today

or

1,000,000 Taka in 5 years1,000,000 Taka in 5 years?

Why time?

Why is time such an important element in your decision?

– Because TIME allows you the opportunity to postpone consumption and earn INTEREST.

Types of interest

• Simple interest– Interest paid on principal sum only.

• Compound interest– Interest paid on the principal and on prior interest that has not been paid or withdrawn.

Simple interest formula

Formula SI = P0(i)(n)

SI: Simple interestP0: Deposit today (at time t =

0)i: Interest rate per periodn: Number of time periods

Simple interest example #1

•Assume that you deposit 100 Taka in an account earning 5% annual simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?

SI = P0(i)(n)

= (Taka 100) (0.05) (2)= Taka 10

Simple interest example #2

•Assume that you deposit 10,000 Taka in an account earning 10% annual simple interest for 5 years. What is the accumulated interest at the end of the 5th year?

SI = P0(i)(n)

= (Taka 10,000) (0.10) (5)= Taka 5,000

Simple interest example #3

•Assume that you deposit 80,000 Taka in an account earning 6.3% annual simple interest for 11 years. What is the accumulated interest at the end of the 11th year?

SI = P0(i)(n)

= (Taka 80,000) (0.063) (11)

= Taka 55,440

Simple interest example #4

•Assume that you deposit 80,000 Taka in an account earning 6.3% annual simple interest for 3 months. What is the accumulated interest at the end of the 3rd month?

SI = P0(i)(n)

= (Taka 80,000) (0.063) (3/12)

= Taka 1,260

Why compound interest?

0

5000

10000

15000

20000

1st Year 10thYear

20thYear

30thYear

Future Value of a Single 1,000 Taka Deposit

10% SimpleInterest7% CompoundInterest10% CompoundInterest

FV: Compound interest

•Assume that you deposit 1,000 Taka at a compound interest rate of 7% for 2 years.

0 1 22

Taka 1,000Taka 1,000FVFV22

7%

FV: Compound interest formula

Formula FVFVnn = P0 (1+i)n

FVFVnn:Future value (after n periods)

P0 : Deposit today (at time t = 0)

i: Interest rate per periodn: The number of time

periods

FV: Compound interest

FVFV1 = PP00 (1+i)1 = Taka 1,0001,000 (1.07) = Taka 1,0701,070

Compound interest

•You earned 70 Taka interest on your 1,000 Taka deposit over the first year.

• This is the same amount you would earn under simple interest.

FV: Compound interest

FVFV11 = PP00 (1+i)1 = Taka Taka 1,0001,000 (1.07)

= Taka Taka 1,0701,070

FVFV22 = FV1 (1+i)1

= PP0 0 (1+i)(1+i) = Taka Taka 1,0001,000(1.07)(1.07)

= PP00 (1+i)2 = Taka Taka 1,0001,000(1.07)2

= Taka Taka 1,144.901,144.90

You earned an extra Taka 4.90 in Year 2 You earned an extra Taka 4.90 in Year 2 with compound over simple interest. with compound over simple interest.

General FV compound interest formula

Formula

FVFV11 = P0 (1+i)1

FVFV22 = P0 (1+i)2

etc

General future value formula

FVFVnn = P0 (1+i)n

or FVFVnn = P0 (FVIFFVIFi,n) -- See See Table ITable I

Valuation using FV table

•FVIFFVIFi,n is found in this table. – You can find this table in your text book. – I will also provide you with one during tests/midterm etc.

Period 6% 7% 8% 1 1.0600 1.0700 1.0800 2 1.1236 1.1449 1.1664 3 1.1910 1.2250 1.2597 4 1.2625 1.3108 1.3605 5 1.3382 1.4026 1.4693

Valuation using FV table

FV2 = Taka 1,000 (FVIFFVIF7%,2)= Taka 1,000 (1.1451.145)

= Taka 1,145

Period 6% 7% 8% 1 1.0600 1.0700 1.0800 2 1.1236 1.1449 1.1664 3 1.1910 1.2250 1.2597 4 1.2625 1.3108 1.3605 5 1.3382 1.4026 1.4693

FV table example #1

0 1 2 3 4 55

10,000 Taka10,000 Taka

FVFV55

6%

Mawa wants to know how large her deposit of 10,00010,000 Taka today will become at a compound annual interest rate of 6% for 5 years.

FV table example #1Mawa wants to know how large her deposit of 10,00010,000 Taka today will become at a compound annual interest rate of 6% for 5 years. Calculation based on general formula:

FVFVnn = P0 (1+i)n

FVFV55 = Taka 10,000 (1+ 0.06)5

= Taka 13,382.26Taka 13,382.26Calculation based on table:

FVFV55 = Taka 10,000 (FVIFFVIF6%, 5)

FVFV55 = Taka 10,000 (1.3382)

= Taka 13,382.00Taka 13,382.00

FV table solution #2Shams wants to know how large his deposit of 10,00010,000 Taka today will become at a compound annual interest rate of 8% for 3 years. Calculation based on general formula:

FVFVnn = P0 (1+i)n

FVFV55 = Taka 10,000 (1+ 0.08)3

= Taka 12,597.12Taka 12,597.12Calculation based on table:

FVFV55 = Taka 10,000 (FVIFFVIF8%, 3)

FVFV55 = Taka 10,000 (1.2597)

= Taka 12,597.00Taka 12,597.00

FV table example #3Marium wants to know how large her deposit of 10,00010,000 Taka today will become at a compound annual interest rate of 7% for 4 years. Calculation based on general formula:

FVFVnn = P0 (1+i)n

FVFV55 = Taka 10,000 (1+ 0.07)4

= Taka 13,107.96Taka 13,107.96Calculation based on table:

FVFV55 = Taka 10,000 (FVIFFVIF7%, 4)

FVFV55 = Taka 10,000 (1.3108)

= Taka 13,108Taka 13,108