1. Effective Personal Financial Planning
Chapter 4

2. Topics
Time Value of money
Simple Interest
Compound interest
The power of compounding
Annuities

3. What is Interest?
When you borrow Money from someone, or use somebody else’s money
You have to pay a rent for using the money
This amount is paid back to the lender along with the original amount borrowed
This is sometimes known as the cost of Money, which doesn’t belong to you, but you have used it

4. What is Interest? This extra amount is called the “INTEREST”
The original amount borrowed is known as the “PRINCIPAL”
The sum of both Principal and the interest is known as “AMOUNT”
There are basically TWO types of Interest:
SIMPLE INTEREST & COMPOUND INTEREST

5. Simple Interest
Simple Interest rate: Interest= P*r*t Where “P” is Principal, “r” is Interest rate, “t ‘ is the time period Note that “r” is in decimal form, i.e. r %/ 100 Example: If ₹ 1000 is invested for 25 10% p.a., then, Interest= 1000*0.1*25 = ₹ 2500 Amount = Principal + Interest = = ₹ 3500

6. Compound interest rate
Interest is added into principal at each compounding period
FV= PV (1+r)^ n
Where “PV” is the principal, “r” is interest rate, “n” is the time period, “ FV” is the future value, or maturity value
Note that “r” is in decimal form, i.e. r %/ 100

7. Compound Interest Rate
Example
If ₹ 1000 is invested for 3 10% p.a. compounding annually, then
Interest for 1st year = 1000 *0.1*1 = 100, so principal at the end of 1st year = = 1100
Interest for 2nd year = 1100*0.1*1 = 110, so principal at the end of the 2nd year = = 1210
Interest for 3rd year = 1210*0.1*1 = 121, so FV = = ₹ 1331
OR Alternatively: FV= 1000*(1+0.1)^3 = ₹ 1331
SIMILARLY, if above is invested for 25 years : FV= 1000*(1+0.1)^25 = ₹ 10,835

8. Compounding impact in the long run
₹ 1000 invested at 10% p.a. simple interest in your saving bank account will fetch you ₹3500 after 25 years
The same ₹ 1000 invested at 10% p.a. compounded will fetch you ₹ 10,385 after 25 years, more than 3 times more than the bank deposit

9. Change in compounding frequency
Compounding Interval
The interest can be compounded at different frequencies during the year, e.g.
Yearly, Semi annually, quarterly, monthly, etc.
Higher the compounding frequency, higher the return on investment

10. Change in compounding frequency
Example:
₹ 100 invested for 1 10% p.a. compounding semi annually, what is the return on investment after one year?
Interest for 1st semi annual period = 100 *0.1* (6/12) = 5
Principal after 1st Semi Annual period = = 105
Interest at the end of 2nd Semi Annual period = 105*0.1*(6/12) = 5.25
So FV after 1 year = = or effectively a 10.25% return.
This return is higher than the stated rate of 10 %

11. Change in compounding frequency
Alternatively use the formula as below for taking into account the compounding frequency
FV = PV( 1+ r/m)^(m*n), where “m” is the compounding frequency
In the previous example
FV = 100* ( /2)^ (2*1) = 100*1.05^2 = or 10.25% return

12. Nominal and Effective Rate
Nominal Rate
It is stated interest rate of a given bond or loan
In the previous example, the nominal rate was 10%
Effective Rate
It is the annual rate that takes the compounding frequency into account
In the previous example, the effective rate was 10.25%

13. The effect of compounding frequency in the long run

14. It is the return on an investment after taking inflation into account
Real Rate of Return
It is the return on an investment after taking inflation into account
1 + Interest Rate
Real Rate of Return =
1 + Inflation Rate

15. Real Rate of Return of Bank FD
Example
If bank FD rate is 8% p.a., inflation is 6% p.a. , and the starting balance is ₹ Using the Real rate of Return formula, this example would show
Real rate of Return = {(1+0.08)/( )}- 1 = 1.887%
With ₹ 1000 starting balance ,then after 1 year, the individual could purchase ₹ of goods based on today’s cost

16. Tax adjusted Real Rate of Return of Bank FD
Where Post tax Return = Nominal Return (1- Tax Rate)
In the previous example, if tax rate is 20%, the post tax return =
0.08 (1- 0.2)= 6.4%
Tax Adjusted Real Rate of return = {(1.064)/(1.06)} -1= 0.377%
1 + Post Tax return
1 + Inflation Rate

17. Tax equivalent yield
Tax Equivalent yield = Post Tax Return or Tax free return/ (1- Tax Rate)
Example: What would be the tax equivalent yield of a 8% tax free bond , the investor falls in the 30% tax category
Tax Equivalent yield = 0.08/ (1-0.3) = 11.43%

18. Would you prefer to have 1 crore now or 1 crore 10 years from now?
Time Value of Money
Would you prefer to have 1 crore now or 1 crore 10 years from now?

19. Time Value of Money The value of money changes with change in time.
A rupee received today is more valuable than a rupee received one year later.
-Present Value concept (PV concept)
-Future or Compounding Value concept (FV concept)

20. Reasons for Time Preference of Money
Uncertain future
Risk involvement
Present needs
Return

21. Time Value of Money The Terminology of Time Value
Present Value (PV) - An amount of money today, or the current value of a future cash flow
Future Value (FV) - An amount of money at some future time period
Period (n) - A length of time (often a year, but can be a quarter, month, etc.)
Interest Rate (r)- The compensation paid to a lender (or saver) for the use of funds expressed as a percentage for a period (normally expressed as an annual rate)

22. Calculation of Future Value (FV)
Future Value of a Single Amount You have Rs.1,000 today and you deposit it with a financial institution, which pays 10 per cent interest compounded annually, for a period of 3 years. What is the total amount after 3 years?

23. Formula
FV =PV×(1+r)n Where: FV = Future value after n years PV = Present Value (cash today) r = Interest rate per annum n = Number of years for which compounding is done

24. Calculating FV via EXCEL
Use Function: FV
Input:
Rate= 10%
Nper= 3
PV= -1000
(outflows are negative)
Output:
FV=₹ 1,331.00

25. Calculation of Present Value
PV =FV / (1+r)n

26. What is the meaning of 1 crore received on retirement after 10 years (assume inflation 6%)
Calculating PV using EXCEL:
Use Function: PV
Input:
Rate=6 %
Nper= 10
FV= 1 crore
Output:
PV=₹ 55.4 lacs

27. Annuities
An Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.

28. Types of Annuities
Ordinary Annuity: Payments or receipts occur at the end of each period.
Annuity Due: Payments or receipts occur at the beginning of each period.

29. Annuity examples SIP Car Loan Payments Insurance Premiums
Housing Loan EMI
Retirement Savings
Monthly Pension
Salary

30. Ordinary Annuity: Example House loan EMI
End of
Period 1
End of
Period 2
End of
Period 3
₹ ₹ ₹ 100
Today
Equal Cash Flows
Each 1 Period Apart

31. Annuity Due: Example monthly pension
Beginning of
Period 1
Beginning of
Period 2
Beginning of
Period 3
₹ ₹ ₹ 100
Today
Equal Cash Flows
Each 1 Period Apart

32. In our calculations we will use Annuity Due
For Investments
For SIP
For insurance premiums
For PF and PPF payments
For receiving monthly pension
IN Excel, T= 1

33. Annuity Problems using EXCEL
n = number of payments or rents
i = interest rate
PMT = Periodic payment (rent) received or paid
And either:
FV of an annuity = Value in the future of a series of future payments OR
PV of an annuity = Value today of a series of payments in the future
When we know any three of the four amounts, we can solve for the fourth! 16 14 16 14 16 16 16 16

34. If I save ₹ 120,000 per year @ 8.5% for next 25 years, how much would I have in Year 25?
Use FV function
N= 25
I = 8.5% or 0.085
PMT = ₹ 1,20,000
T = 1
FV= ?
Solve for FV = 102,42, 546
Answer= ₹ 1 crore

35. And what would be the meaning of that 1 crore today, assuming inflation is 6 percent
Use PV function
N= 25
I = 6% or 0.06
FV = ₹ 1,00,00, 000
T= ignore, use only with PMT
PV= ?
Solve for PV = 23,29, 988
Answer= ₹ 23.3 lacs

36. Another question
Shom plans the marriage of his son after 20 years. Today the marriage would cost him 30 lacs. What monthly instalment should he invest from now at 12 %, assuming inflation of expenses at 6%.

37. Shom question Solve in 2 steps: Step 1
What is the value of marriage expenses after 20 years?
Use function FV
N= 20
Inflation. i= 6%, i.e. 0.06
PV= - 30,00,000
FV= ?, Solve FV= 96,21,406

38. Step 2
How much should he invest per month starting now, to achieve the goal?
Use function PMT
N=20*12 periods (monthly)
Interest i = 12%/12 (interest per period)
FV= 96,21,406
T= 1 (it involves PMT!)
PMT= ? Solve for PMT, = per month
Shom needs to invest 9630 per month for next 20 years to meet the goal of his son’s marriage

39. Recap for STEP 2: Change in compounding frequency
Alternatively use the formula as below for taking into account the compounding frequency
FV = PV( 1+ r/m)^(m*n), where “m” is the compounding frequency
In the previous example
FV = 100* ( /2)^ (2*1) = 100*1.05^2 = or 10.25% return

40. Classwork Project 1 of your lumpsum financial goal to the future.
How much would you need to invest on a monthly basis to achieve it

41. Home work Project all your financial goals to the future.
How much would you need to invest on a monthly/ yearly basis to achieve them, Calculate amount per goal

42. Further reading