mac2602Topic 3 - Time value of money.pdf - 47 TOPIC 3 Time value of money concepts and mathematical formulae Study unit 8 – TVM concepts and

mac2602Topic 3 - Time value of money.pdf - 47 TOPIC 3 Time...

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47 MAC2602 Russell Jude © Edge Business School uni0054uni004Funi0050uni0049uni0043uni0009uni0033uni003A Time value of money concepts and mathematical formulae Study unit 8 – TVM concepts and mathematical formulae Study unit 9 – Alternative methodologies for solving TVM problems Cash flow definitions Single cash flows Once off cash flow Ordinary annuity A series of repetitive cash flows which occur at the end of fixed intervals for a specific number of periods Annuity due A series of repetitive cash flows which occur at the beginning of fixed intervals for a specific number of periods Perpetuity Repetitive cash flows which continue forever Unequal cash flows Unequal cash flows for a number of periods Types of interest Simple interest = interest calculated on the principal amount only Compound interest = interest is calculated on the principal amount and the interest earned in the previous period Example 1: You inherited R50 000 from your grandmother and decided to invest the money in a bank account that earns 10% interest per annum. Determine the value of your investment after 3 years if: a) The 10% is simple interest b) The 10% is compounded annually
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48 MAC2602 Russell Jude © Edge Business School Solution 1: a) Simple interest Year Interest calc Interest Balance calc Balance 1 2 3 50 000 x 10% 50 000 x 10% 50 000 x 10% 5 000 5 000 5 000 50 000 + 5 000 55 000 + 5 000 60 000 + 5 000 55 000 60 000 65 000 OR Opening balance 50 000 Interest 50 000 x 10% x 3 years = 15 000 Closing balance 65 000 b) Compounded interest Year Interest calc Interest Balance calc Balance 1 2 3 50 000 x 10% 55 000 x 10% 60 500 x 10% 5 000 5 500 6 050 50 000 + 5 000 55 000 + 5 500 60 500 + 6 050 55 000 60 500 66 550 OR Use your financial calculator: PV = 50 000 I = 10% N = 3 Pmt = 0 FV = -66 550 Future value Future value of a single amount Formula Table Financial calculator FV = PV x (1+i) n Where: FV = Future value PV = Present value i = Interest rate n = No of periods FV = PV x FV factor Use table C to obtain the FV factor PV = Single amount N = Number of periods i = Interest rate Pmt = 0 Compute the FV Do NOT use your financial calculator
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49 MAC2602 Russell Jude © Edge Business School Example 2: FV of a single amount A person would like to invest R10 000 at 15% per annum. What will the value be after: 1. 1 year if interest is compounded annually? 2. 3 years if interest is compounded annually? 3. 3 years if interest is compounded monthly? Solution: Formula Tables Calculator 1. FV = PV x (1 + i) n = 10 000 x (1 + 0.15)¹ Solution: FV = R11 500 1. Table C (i = 15, n = 1) Factor = 1.15 FV = 10 000 x 1.15 Solution: FV = R11 500 1. PV = 10 000 n = 1 i = 15 Solution: FV = R11 500 2. FV = PV x (1 + i) n = 10 000 x (1 + 0.15)³ Solution: FV = R15 209 2. Table C (i = 15, n = 3) Factor = 1.5209 FV = 10 000 x 1.5209 Solution: FV = R15 209 2. PV = 10 000 n = 3 i = 15 Solution: FV = R15 209 3. FV = PV x (1 + i) n = 10 000 x (1 + 0.15/12)³⁶ Solution: FV = R15 639 3. 15/12 = 1.25% not on table Calculate the factor using the last bit of the formula: The factor = (1 + i) n = (1 + 0.15/12)³⁶ = 1.5639 Therefore FV = 10 000 x 1.5639 FV = 15 639 3.
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