compounding and discounting

Basic Introduction

1. COMPOUNDING AND Discounting B.COM CC204 SEMESTER 2 UNIT 3 (Mathematics of finance) BUSINESS MATHEMATICS AND STATISTICS By : CS REENA KUMARI Assistant professor Department of Commerce PATNA WOMEN’S COLLEGE (Autonomous) Email id: [email protected]

2. INDEx BY CS REENA KUMARI

3. Time value of money 1 ) It is defined as a concept which states that purchasing power of money declines with the passage of time. Inflation is the reason for fall in the purchasing power of money. Due to inflation a given amount of money buys fewer goods in the future than it will now. 2) Time value of money means that the value of a unity of money is different in different time periods. The sum of money received in future is less valuable than it is today. In other words the present worth of money received after some time will be less than a money received today. Since a money received today has more value rational investors would prefer current receipts to future receipts. If they postpone their receipts, they will certainly charge some money i.e. interest. BY CS REENA KUMARI

4. Compounding BY CS REENA KUMARI

5. Discounting Discounting is the process of converting the future amount into its Present Value. The current value of the given future value is known as Present Value. The discounting technique helps to ascertain the present value of future cash flows by applying a discount rate. The following formula is used to know the present value of a future sum: Where 1,2,3,…..n represents future years FV = Future Cash flows generated in different years, R = Discount Rate BY CS REENA KUMARI

6. Discounting rate A  discount rate  is the  rate  of return used to  discount  future cash flows back to their present value. BY CS REENA KUMARI

7. Conversion period The various conversion periods are given below : The period at the end of which the interest is compounded is called conversion period. Example :- When the interest is calculated and added to the principal every six months the conversion period is six months. Conversion period Description Number of conversion period in a year 1 day Compounded daily 365 1 month Compounded monthly 12 3 months Compounded quarterly 4 6 months Compounded semi annually 2 12 months Compounded annually 1 BY CS REENA KUMARI

8. Formulas Where in , i = interest rate n = no. of conversion periods t = time BY CS REENA KUMARI

9. Relationship between compounding and discounting The concept of compounding and discounting are similar in the sense that discounting brings a future sum of money to the present time using a discount rate and compounding brings a present sum of money to future time. BY CS REENA KUMARI

10. Difference between compounding and discounting Compounding Meaning : The method used to determine the future value of present investment is known as Compounding. Concept : If we invest some money today ,what will be the amount we get at a future date. Use of : COMPOUND INTEREST RATE Also known as : Future Value Technique discounting The method used to determine the present value of future cash flows is known as Discounting. If we want a certain sum of money in future ,how much amount should be invested at present. DISCOUNTING RATE Present Value Technique BY CS REENA KUMARI

11. Practical sum 1 (compounding) Assume you put Rs.10,000 in a bank for interest rate of 5 %.How much money will bank give you after 5 years? Solution, It is a basic sum of compounding. Future value = Present value (1 + i) n = 10000 (1 + 0.05 )5 = 10000 x 1.2763 =Rs. 12,763/- Note : Sometimes ,the value of (1.05) 5 will be given in sum. If not, calculate it. Year 1 1.05 x1 = 1.05 Year 2 1.05 x1.05 = 1.1025 Year 3 1.05 x1.1025 = 1.57625 Year 4 1.05 x1.57625= 1.2155 Year 5 1.05 x1.2155 = 1.27628 or 1.2763 BY CS REENA KUMARI

12. Practical sum 2 (discounting) Lets suppose Mr Z require Rs.1,00,000/- after 5 years ,Market interest rate is 10%.Advise Mr Z how much amount he should invest now to get Rs.1,00,000/- after 5 years. Solution , The sum is based on calculation of present value. Method 1 : By formula ,PV = FV = 100000 = 100000 = Rs.62,092/- (1 + i) n ( 1+ 10 )5 (1.1 )5 100 Interpretation : If Mr Z invest Rs.62,092 at present at 10% for 5 years. He will get Rs.1,00,000/- after 5 years. Note : Check answer : 62092 (1+0.1)5 =99999.786 =Rs.1,00,000/- BY CS REENA KUMARI

13. Solving the previous sum using discounting rate Method 2 : Calculate discounting rate /factor of 10% for the 5 th year. Dn = 1 / (1+i) n D 5 = 1/ (1+ 0.1) 5 = 0.62092 is the discounting factor of 10 % for 5th year. Calculate PV =FV x d f (Discounting rate /factor) =1,00,000 x .62092 = Rs.62,092/- Note 1 : Answer will be same by both the methods. Note 2 : Sometimes, value of discounting factor given in the sum, if not use formula to calculate. BY CS REENA KUMARI

14. Practical sum 3 (Calculating discounting factor) Calculate the discounting factor of 10 % for the 5 years. (Dn = 1/(1+ i) n) Year Rate Formula Df 1 10 % 1 / (1+ 0.1 ) 1 0.909 2 10 % 1 / (1+ 0.1 ) 2 0.826 3 10 % 1 / (1+ 0.1 ) 3 0.751 4 10 % 1 / (1+ 0.1 ) 4 0.683 5 10 % 1 / (1+ 0.1 ) 5 0.621 Sum of Annuity =.909+0.826+0.751+0.683+0.621=3.79 –sum of annuity of 10% for 5 years BY CS REENA KUMARI

15. KEEP LEARNING ,HAPPY LEARNING BY CS REENA KUMARI