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Effective Personal Financial Planning

Gain insights into Simple and Compound Interest, the Power of Compounding, Annuities, and the impact of compounding frequency on investments for effective personal financial planning.

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Effective Personal Financial Planning

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  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 years @ 10% p.a., then, Interest= 1000*0.1*25 = ₹ 2500 Amount = Principal + Interest = 1000 +2500 = ₹ 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 years @ 10% p.a. compounding annually, then • Interest for 1st year = 1000 *0.1*1 = 100, so principal at the end of 1st year = 1000 + 100 = 1100 • Interest for 2nd year = 1100*0.1*1 = 110, so principal at the end of the 2nd year = 1100 + 110 = 1210 • Interest for 3rd year = 1210*0.1*1 = 121, so FV = 1210 + 121 = ₹ 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 year @ 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 = 100 + 5 = 105 Interest at the end of 2nd Semi Annual period = 105*0.1*(6/12) = 5.25 So FV after 1 year = 105 +5.25 = 110.25 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* (1 + 0.1/2)^ (2*1) = 100*1.05^2 = 110.25 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. Real Rate of Return It is the return on an investment after taking inflation into account 1 + Interest Rate Real Rate of Return = ----------------------- - 1 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 ₹ 1000. Using the Real rate of Return formula, this example would show • Real rate of Return = {(1+0.08)/(1+ 0.06)}- 1 = 1.887% • With ₹ 1000 starting balance ,then after 1 year, the individual could purchase ₹ 1018.17 of goods based on today’s cost

  16. Tax adjusted Real Rate of Return of Bank FD • Tax adjusted Real Rate of Return = • 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 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. 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 2 (Ordinary Annuity) End of Period 1 End of Period 3 0 1 2 3 ₹ 100 ₹ 100 ₹ 100 Equal Cash Flows Each 1 Period Apart Today

  31. Annuity Due: Example monthly pension Beginning of Period 2 (Annuity Due) Beginning of Period 1 Beginning of Period 3 0 1 2 3 ₹ 100 ₹ 100 ₹ 100 Equal Cash Flows Each 1 Period Apart Today

  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!

  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, = - 9630 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* (1 + 0.1/2)^ (2*1) = 100*1.05^2 = 110.25 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

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