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![The “Rule-of-72”
Approx. Years to Double = 72 / i%
QUICK!!
How long does it take to double 150,000 Taka at a
compound interest rate of 12% per year?
72 / 12% = 6 years
[Actual time is 6.12 years]](https://image.slidesharecdn.com/timevalueofmoneypart2-201204194449/75/Time-value-of-money-part2-2-2048.jpg)
Uploaded bySudipta Saha
Time value of money part2
The document discusses time value of money concepts including compound interest, present value, future value, and annuities. It provides examples of how to calculate: - Future and present value of a single cash flow using the compound interest formula and present/future value tables - Future and present value of an ordinary annuity and annuity due using the annuity formulas and present/future value tables - Number of periods for a cash flow to double using the rule of 72
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Time value of money part2
- 1. Time value ofmoney Part 2
- 2. The “Rule-of-72” Approx. Yearsto Double = 72 / i% QUICK!! How long does it take to double 150,000 Taka at a compound interest rate of 12% per year? 72 / 12% = 6 years [Actual time is 6.12 years]
- 3.
- 4. PV: Compound interest •Assumethat you need 1,000 Taka in 2 years. How much do you need to deposit today at a discount rate of 7% compounded annually? 0 1 2 7% Taka 1,000 PV1PV0
- 5. PV: Compound interestformula Formula PV0 = FVn / (1+i)n PV0: Present value (at time 0) FVn: Future value after n time periods i: Interest rate per period n: The number of time periods
- 6. PV: Compound interest PV0= FV2 / (1+i)2 = $1,000 / (1.07)2 = FV2 / (1+i)2 = $873.44 0 1 2 7% Taka 1,000 PV1PV0
- 7. General PV compoundinterest formula Formula PV0 = FV1 / (1+i)1 PV0 = FV2 / (1+i)2 etc General present value formula PV0 = FVn / (1+i)n or PV0 = FVn (PVIFi,n) -- See Table II
- 8. Valuation using PVtable •PVIFi,n is found in this table. – You can find this table in your text book. – I will also provide you with one during tests/midterm etc. Period 6% 7% 8% 1 .9434 .9346 .9259 2 .8900 .8734 .8573 3 .8396 .8163 .7938 4 .7921 .7629 .7350 5 .7473 .7130 .6806
- 9. Valuation using PVtable PV2 = Taka 1,000 (PVIF7%,2) = Taka 1,000 (.8734) = Taka 873.40 Period 6% 7% 8% 1 .9434 .9346 .9259 2 .8900 .8734 .8573 3 .8396 .8163 .7938 4 .7921 .7629 .7350 5 .7473 .7130 .6806
- 10. PV table example#1 Shovon wants to know how large a deposit to make so that the money will grow to 10,000 Taka in 5 years at a discount rate of 6%. 0 1 2 3 4 5 10,000 Taka PV0 6%
- 11. PV table solution#1 Shovon wants to know how large a deposit to make so that the money will grow to 10,000 Taka in 5 years at a discount rate of 6%. Calculation based on general formula: PV0 = FVn / (1+i)n PV0 = Taka 10,000 / (1+ 0.06)5 = Taka 7,472.58 Calculation based on table: PV0 = Taka 10,000 (PVIF6%, 5) = Taka 10,000 (.7473) = Taka 7,473.00
- 12. PV table example#2 Marjan wants to know how large a deposit to make so that the money will grow to 10,000 Taka in 3 years at a discount rate of 8%. Calculation based on general formula: PV0 = FVn / (1+i)n PV0 = Taka 10,000 / (1+ 0.08)3 = Taka 7,938.32 Calculation based on table: PV0 = Taka 10,000 (PVIF8%, 3) = Taka 10,000 (.7938) = Taka 7,938.00
- 13. PV table example#3 Galib wants to know how large a deposit to make so that the money will grow to 10,000 Taka in 4 years at a discount rate of 7%. Calculation based on general formula: PV0 = FVn / (1+i)n PV0 = Taka 10,000 / (1+ 0.07)4 = Taka 7,628.95 Calculation based on table: PV0 = Taka 10,000 (PVIF7%, 4) = Taka 10,000 (.7629) = Taka 7,629.00
- 14. Annuities An Annuity representsa series of equal payments (or receipts) occurring over a specified number of equidistant periods.
- 15. Types of annuities •Ordinaryannuity: Payments or receipts occur at the end of each period. •Annuity due: Payments or receipts occur at the beginning of each period.
- 16. Examples of annuities •InsurancePremiums •Retirement Savings (Provident Fund) •Student Loan Payments •Car Loan Payments •Mortgage Payments
- 17. Parts of anannuity 0 1 2 3 Tk. 100 Tk. 100 Tk. 100 End of Period 1 End of Period 2 Today Equal Cash Flows Each 1 Period Apart End of Period 3 Ordinary Annuity
- 18. Parts of anannuity 0 1 2 3 Tk.100 Tk.100 Tk.100 Beginning of Period 1 Beginning of Period 2 Today Equal Cash Flows Each 1 Period Apart Beginning of Period 3 Annuity Due
- 19. Overview of anordinary annuity - FVA FVAn = R(1+i)n-1 + R(1+i)n-2 + ... + R(1+i)1 + R(1+i)0 R R R 0 1 2 n n+1 FVAn R = Periodic Cash Flow Cash flows occur at the end of the period i% . . .
- 20. Example of anordinary annuity - FVA FVA3 = $1,000(1.07)2 + $1,000(1.07)1 + $1,000(1.07)0 = $1,145 + $1,070 + $1,000 = $3,215 $1,000 $1,000 $1,000 0 1 2 3 4 $3,215 = FVA3 7% $1,070 $1,145 Cash flows occur at the end of the period
- 21. Hint on annuityvaluation The future value of an ordinary annuity can be viewed as occurring at the end of the last cash flow period, whereas the future value of an annuity due can be viewed as occurring at the beginning of the last cash flow period.
- 22. Valuation using TableIII FVAn = R (FVIFAi%,n) FVA3 = $1,000 (FVIFA7%,3) = $1,000 (3.2149) = $3,214.90 Period 6% 7% 8% 1 1.0000 1.0000 1.0000 2 2.0600 2.0700 2.0800 3 3.1836 3.2149 3.2464 4 4.3746 4.4399 4.5061 5 5.6371 5.7507 5.8666
- 23. Overview of anannuity due - FVAD FVADn = R(1+i)n + R(1+i)n-1 + ... + R(1+i)2 + R(1+i)1 = FVAn (1+i) R R R R R 0 1 2 3 n-1 n FVADn i% . . . Cash flows occur at the beginning of the period
- 24. Example of anannuity due – FVAD FVAD3 = $1,000(1.07)3 + $1,000(1.07)2 + $1,000(1.07)1 = $1,225.04 + $1,144.90 + $1,070.00 = $3,439.94 $1,000 $1,000 $1,000 $1,070.00 0 1 2 3 4 $3,439.94 = FVAD3 7% $1,225.04 $1,144.90 Cash flows occur at the beginning of the period
- 25. Valuation using TableIII FVADn = R (FVIFAi%,n)(1+i) FVAD3 = $1,000 (FVIFA7%,3)(1.07) = $1,000(3.2149)(1.07) = $3,439.94 Period 6% 7% 8% 1 1.0000 1.0000 1.0000 2 2.0600 2.0700 2.0800 3 3.1836 3.2149 3.2464 4 4.3746 4.4399 4.5061 5 5.6371 5.7507 5.8666
- 26. Overview of anordinary annuity – PVA PVAn = R/(1+i)1 + R/(1+i)2 + ... + R/(1+i)n R R R 0 1 2 n n+1 PVAn R = Periodic Cash Flow i% . . . Cash flows occur at the end of the period
- 27. Example of anordinary annuity – PVA PVA3 = $1,000/(1.07)1 + $1,000/(1.07)2 + $1,000/(1.07)3 = $934.58 + $873.44 + $816.30 = $2,624.32 $1,000 $1,000 $1,000 0 1 2 3 4 $2,624.32 = PVA3 7% $ 934.58 $ 873.44 $ 816.30 Cash flows occur at the end of the period
- 28. Hint on annuityvaluation The present value of an ordinary annuity can be viewed as occurring at the beginning of the first cash flow period, whereas the present value of an annuity due can be viewed as occurring at the end of the first cash flow period.
- 29. Valuation using TableIV PVAn = R (PVIFAi%,n) PVA3 = $1,000 (PVIFA7%,3) = $1,000 (2.6243) = $2,624.30 Period 6% 7% 8% 1 0.9434 0.9346 0.9259 2 1.8334 1.8080 1.7833 3 2.6730 2.6243 2.5771 4 3.4651 3.3872 3.3121 5 4.2124 4.1002 3.9927
- 30. Overview of anannuity due - PVD PVADn = R/(1+i)0 + R/(1+i)1 + ... + R/(1+i)n-1 = PVAn (1+i) R R R R 0 1 2 n-1 n PVADn R: Periodic Cash Flow i% . . . Cash flows occur at the beginning of the period
- 31. Example of anannuity due – PVAD PVADn = $1,000/(1.07)0 + $1,000/(1.07)1 + $1,000/(1.07)2 = $2,808.02 $1,000.00 $1,000 $1,000 0 1 2 3 4 $2,808.02 = PVADn 7% $ 934.58 $ 873.44 Cash flows occur at the beginning of the period
- 32. Valuation using TableIV PVADn = R (PVIFAi%,n)(1+i) PVAD3 = $1,000 (PVIFA7%,3)(1.07) = $1,000 (2.6243)(1.07) = $2,808.00 Period 6% 7% 8% 1 0.9434 0.9346 0.9259 2 1.8334 1.8080 1.7833 3 2.6730 2.6243 2.5771 4 3.4651 3.3872 3.3121 5 4.2124 4.1002 3.9927
- 33. Steps to solveTVM problems 1. Read problem thoroughly 2. Determine if it is a PV or FV problem 3. Create a time line 4. Put cash flows and arrows on time line 5. Determine if solution involves a single CF, annuity stream(s), or mixed flow 6. Solve the problem 7. Check with financial calculator (optional)