1. Accounting & Finance for Bankers - Business Mathematics- Module A SPBT College

2. Simple Interest

3. More Simple Interest …

4. Compound Interest: A FV Perspective

5. Compounding …

6. Time Line: Rs78.35 Invested (5 Years, 5% Interest) 0 1 2 3 4 5 PV = Rs78.35 FV 5 = Rs100 End of Year

7. Future Value of Rs200 (4 Years, 8% Interest ) 0 1 2 3 4 PV = Rs200 End of Year FV 1 = Rs216 FV 2 = Rs233.28 FV 3 = Rs251.94 FV 4 = Rs272.10 Compounding – the process of earning interest in each successive year

8. FV of a Mixed Cash Flow Stream (5 Years, 5.5% Interest) FV 5 = Rs16,689.06 0 1 2 3 4 5 Rs3,500 Rs3,800 Rs2,000 Rs3,000 Rs2,500 Rs4,335.89 Rs4,462.12 Rs2,226.06 Rs3,165.00 Rs2,500.00 End of Year

9. Future Value Example

10. Power Of Compound Interest Periods 0% Future Value of One Rs) 1.00 0 2 4 6 8 10 12 14 16 18 20 22 24 10.00 15.00 20.00 25.00 30.00 5.00 10% 5% 15% 20%

11. Format of a Future Value Interest Factor (FVIF) Table

12. Computing Future Values Using Excel Excel Function =FV (interest, periods, pmt, PV) =FV (.03, 5,,1000) You deposit Rs1,000 today at 3% interest. How much will you have in 5 years?

13. Present Value with Compounding

14. Present Value of Rs500 (7 Years, 6% Discount Rate) 0 1 2 3 4 5 6 7 PV = Rs332.53 FV 7 = Rs500 End of Year

15. Present Value of Future Amounts Present Value of Future Amounts (4 Years, 7% Interest ) 0 1 2 3 4 Discounting PV = Rs200 FV1 = Rs214 FV2 = Rs228.98 FV3 = Rs245 FV4 = Rs262.16 End of Year

16. PV of a Mixed Stream (4 Years, 6% Interest) Rs1,500,000 Rs3,000,000 Rs2,000,000 Rs5,000,000 End of Year PV 4 = Rs9,724,500 Rs1,415,100 Rs2,669,700 Rs1,679,200 Rs3,960,500 0 1 2 3 4

17. Present Value Examples

18. Format of a Present Value Interest Factor (PVF) Table

19. Calculating PV Of A Single Amount Using Excel Example: How much must you deposit today in order to have Rs500 in 7 years if you can earn 6% interest on your deposit? Excel Function =PV (interest, periods, pmt, FV) =PV (.06, 7,,500)

20. W. P. Carey Executive MBA ProgramSlide 20 FV & PV of Mixed Stream (5 Years, 4% Interest Rate) PV Rs5,271.7 0 1 2 3 4 5 -Rs10,000 Rs3,000 Rs5,000 Rs4,000 Rs3,000 Rs2,000.0 Discounting End of Year FV Rs6,413.8 Compounding - Rs12,166.5 Rs3,509.6 Rs5,624.3 Rs4,326.4 Rs3,120.0 Rs4,622.8 Rs3,556.0 Rs2,564.4 Rs1,643.9 Rs2,884.6

21. Annuity Cash Flows

22. FV of Ordinary Annuity FV of Ordinary Annuity (End of 5 Years, 5.5% Interest Rate) 0 1 2 3 4 5 Rs1,000 Rs1,000 Rs1,000 Rs1,000 Rs1,000 Rs1,238.82 Rs1,174.24 Rs1,113.02 Rs1,055.00 Rs1,000.00 End of Year

23. FV of an Ordinary Annuity Using Excel Excel Function =FV (interest, periods, pmt, PV) =FV (.043, 5,1000 ) How much will your deposits grow to at the end of five years if you deposit Rs1,000 at the end of each year at 4.3% interest for 5 years?

24. Rs1,000 Rs1,000 Rs1,000 Rs1,000 Rs1,000 End of Year Rs947.87 Rs898.45 Rs851.61 Rs807.22 0 1 2 3 4 5 Rs765.13 PV of Ordinary Annuity PV of Ordinary Annuity (5 Years, 5.5% Interest)

25. Annuity Examples

26. Ordinary Annuity vs. An Annuity Due Annual Cash Flows 0Rs 0Rs1,000 11,000 2 3 4 5 0 TotalRs5,000 End of year a Annuity A (ordinary) Annuity B (annuity due) a The ends of years 0, 1,2, 3, 4 and 5 are equivalent to the beginnings of years 1, 2, 3, 4, 5, and 6 respectively

27. Calculating the Future Value of an Annuity Due Equation for the FV of an ordinary annuity can be converted into an expression for the future value of an annuity due, FVA n (annuity due), by merely multiplying by (1 + r)

28. FV of an Annuity Due Using Excel How much will your deposits grow to at the end of five years if you deposit Rs1,000 at the beginning of each year at 4.3% interest for 5 years? Excel Function =FV (interest, periods, pmt, PV) =FV (.043, 5, 1000) =Rs5,448.89*(1.043)

29. Deposits Needed to Accumulate a Future Sum A person wishes to buy a house 5 years from now and estimates an initial down payment of Rs35,000 will be required at that time She wishes to make equal annual end-of-year deposits in an account paying annual interest of 4 percent, so she must determine what size annuity will result in a lump sum equal to Rs35,000 at the end of year 5 Find the annual deposit required to accumulate FVAn dollars, given an interest rate, r, and a certain number of years, n by solving equation PMT:

30. Loan Amortization Table (10% interest, 4 Year Term) Payments 1Rs1,892.82Rs6,000.00Rs600.00Rs1,292.82Rs4,707.1 8 21,892.824,707.18470.721,422.103,285.08 31,892.823,285.08328.511,564.311,720.77 41,892.821,720.77172.081,720.74-a-a End of year a Due to rounding, a slight difference (Rs.03) exists between beginning-of-year 4 principal (in column 2) and the year-4 principal payment (in column 4) Loan Payment (1) Beginning- of-year principal (2) Interest [.10 x (2)] (3) Principal [(1) – (3)] (4) End-of-year principal [(2) – (4)] (5)