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1. Time value of money
Part 1

2. Time value of money
Obviously, 1,000,000 Taka today.
You already recognize that there is TIME
VALUE TO MONEY!!
Which would you prefer –
1,000,000 Taka today
or
1,000,000 Taka in 5 years?

3. Why time?
Why is time such an important element in your
decision?
– Because TIME allows you the opportunity to
postpone consumption and earn INTEREST.

4. 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interest that has not been paid or withdrawn.

5. Simple interest formula
Formula SI = P0(i)(n)
SI: Simple interest
P0: Deposit today (at time t = 0)
i: Interest rate per period
n: Number of time periods

6. 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

7. 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

8. 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

9. 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

10. Why compound interest?
0
5000
10000
15000
20000
1st Year 10th
Year
20th
Year
30th
Year
Future Value of a Single 1,000 Taka Deposit
10% Simple
Interest
7% Compound
Interest
10% Compound
Interest

11. FV: Compound interest
•Assume that you deposit 1,000 Taka at a
compound interest rate of 7% for 2 years.
0 1 2
Taka 1,000
FV2
7%

12. FV: Compound interest formula
Formula FVn = P0 (1+i)n
FVn: Future value (after n periods)
P0 : Deposit today (at time t = 0)
i: Interest rate per period
n: The number of time periods

13. FV: Compound interest
FV1 = P0 (1+i)1 = Taka 1,000 (1.07)
= Taka 1,070
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.

14. FV: Compound interest
FV1 = P0 (1+i)1 = Taka 1,000 (1.07)
= Taka 1,070
FV2 = FV1 (1+i)1
= P0 (1+i)(1+i) = Taka 1,000(1.07)(1.07)
= P0 (1+i)2 = Taka 1,000(1.07)2
= Taka 1,144.90
You earned an extra Taka 4.90 in Year 2 with
compound over simple interest.

15. General FV compound interest formula
Formula
FV1 = P0 (1+i)1
FV2 = P0 (1+i)2
etc
General future value formula
FVn = P0 (1+i)n
or FVn = P0 (FVIFi,n) -- See Table I

16. Valuation using FV table
•FVIFi,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

17. Valuation using FV table
FV2 = Taka 1,000 (FVIF7%,2)
= Taka 1,000 (1.145)
= 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

18. FV table example #1
0 1 2 3 4 5
10,000 Taka
FV5
6%
Mawa wants to know how large her deposit of 10,000
Taka today will become at a compound annual
interest rate of 6% for 5 years.

19. FV table example #1
Mawa wants to know how large her deposit of 10,000
Taka today will become at a compound annual
interest rate of 6% for 5 years.
Calculation based on general formula:
FVn = P0 (1+i)n
FV5 = Taka 10,000 (1+ 0.06)5
= Taka 13,382.26
Calculation based on table:
FV5 = Taka 10,000 (FVIF6%, 5)
FV5 = Taka 10,000 (1.3382)
= Taka 13,382.00

20. FV table solution #2
Shams wants to know how large his deposit of 10,000
Taka today will become at a compound annual
interest rate of 8% for 3 years.
Calculation based on general formula:
FVn = P0 (1+i)n
FV5 = Taka 10,000 (1+ 0.08)3
= Taka 12,597.12
Calculation based on table:
FV5 = Taka 10,000 (FVIF8%, 3)
FV5 = Taka 10,000 (1.2597)
= Taka 12,597.00

21. FV table example #3
Marium wants to know how large her deposit of
10,000 Taka today will become at a compound
annual interest rate of 7% for 4 years.
Calculation based on general formula:
FVn = P0 (1+i)n
FV5 = Taka 10,000 (1+ 0.07)4
= Taka 13,107.96
Calculation based on table:
FV5 = Taka 10,000 (FVIF7%, 4)
FV5 = Taka 10,000 (1.3108)
= Taka 13,108