This document discusses time value of money concepts like interest, interest rates, equivalence, and cash flow diagrams. It provides examples of calculating interest on loans and investments over time at different interest rates. It also discusses equivalence and retirement planning examples comparing investing small amounts each year versus delaying investments. Constructing cash flow diagrams is introduced as a way to visualize money flows over time under different scenarios.

1. Interest and Equivalence
Class 3

2. Time Value of Money
• By investing Money today, you can
accumulate more money tomorrow
• Interest = Amount Accumulated – Original
Investment
• Interest = Present Amount Owed –
Original Loan

3. Interest Rate
• Percent Interest Rate =
– 100% x (Interest Accrued)/(Original Amount)
• E.g:
– You Borrow Rs. 20,000@15% interest
– Interest after one year = 20,000x0.15=Rs.3000
– Total amount owed after 1 year = Rs. 23,000

4. Equivalence
• What sum of money tomorrow would be
equivalent to a given sum today?
• E.g: Compare the following options. The
prevailing interest rate is 12%
– Rs. 100 today
– Rs. 112 a year from today
• What should you have lent last year to
receive Rs. 112 next year?

5. Pay Rs. 5000 over 5 years@15%
• Option 1: Pay at the end of year 5
End of Yr Interest Total
Owed
Payment Balance
1 750 5750 0 5750
2 862.5 6612.5 0 6612.5
3 991.88 7604.4 0 7604.4
4 1140.7 8745 0 8745
5 1311.8 10056.8 10056.8 0

6. Pay Rs. 5000 over 5 years@15%
• Option 2: Pay Interest and 20% of principal
every year
End of Yr Interest Total
Owed
Payment Balance
1 750 5750 1750 4000
2 600 4600 1600 3000
3 450 3450 1450 2000
4 300 2300 1300 1000
5 150 1150 1150 0

7. Retirement Planning
• Which would you rather do @12%?
– Invest Rs. 2610 every year for the first 6 years
and withdraw the total amount accrued after
40 years?
– Do not invest the first 6 years and invest Rs.
2600 per year for the next 34 years?
• Both are equivalent to Rs. 10,00,000!
• Investments approximately double at:
– 72/(rate of interest) years

8. Cash Flow Diagrams
• P = Value of Money at the Present Time
• F = Value of Money at a Future Time
• A = series of equal end-of-year amounts
of money
• n = number of interest periods
• i = Interest rate per interest period

9. Construct a Cash Flow Diagram
• You plan to borrow Rs. 2000 today and
want to find out how much you should
repay after 5 years at a 12% rate of
interest?
P=2000
F=?
i=12%
0 1 2 3 4 5

10. Construct a Cash Flow Diagram
• What should you deposit 2 years from now
to withdraw Rs. 400 per year for 5 years
starting 3 years from now@15%
P=?
i=15%
0 1 2 3 4 55 6 7
A=400
A AAAA

11. In Class Exercise
• Your friend tells you that he has just
repaid a loan he got 3 years ago at 10%
per year. You learn that he has just paid
Rs. 200. How much did he borrow?
• P = F/[(1+i)^n]
– P= 200/(1.10^3)
– P= Rs. 150

12. In Class Exercise
• Draw the cash-flow diagram
• You want to make 2 equal lump-sum
deposits, one 2 years from now and the
second 4 years from now, so you can
make 5 Rs. 100 withdrawals starting when
the second deposit is made. You also plan
to withdraw an additional Rs. 500, a year
after the withdrawal series ends

13. Thank You