5FIN 300 Time Value Lump Sum Ch 5_6 - FIN 300 Fundamentals of Finance Time Value of Money Lump-Sum Problems Chapters 5 6 FIN 300 TVM Lump Sum 1 Compound

5FIN 300 Time Value Lump Sum Ch 5_6 - FIN 300 Fundamentals...

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FIN 300 Fundamentals of Finance Time Value of Money Lump-Sum Problems Chapters 5 & 6 1 FIN 300 - TVM Lump Sum
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Compound Interest Let’s invest $100 for 2 years, earning a 10% interest rate (or, return) per year How much will we have after 2 years? Answer…….. FIN 300 - TVM Lump Sum 2
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Compound Interest Answer is $121! Let’s break down the math… Start out at t=0, invest $100 After 1 year, we have the original $100 + 10% interest on the $100 = $100 + $10 = $110 Assume we invest the full $110 again for the second year (no withdrawal) After 2 years, we have the original $100, the 1 st year’s interest of $10, the 2 nd year’s 10% interest on the original $100 investment (which gives us $10 in additional interest), and finally, the 2 nd year’s 10 % interest on the 1 st year’s $10 in interest (which adds $1 ) FIN 300 - TVM Lump Sum 3
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Compound Interest Let’s break down the $121 amount….. The $100 amount is called? The $21 amount is called? The $20 amount is called? The $1 amount is called? The $121 is called? FIN 300 - TVM Lump Sum 4
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Compound Interest The $100 amount is the principal, aka. the present value (PV) The $21 amount is the (total) interest The $20 amount is the simple interest The $1 amount is the compound interest, or the interest on the interest The $121 amount is the future value FIN 300 - TVM Lump Sum 5
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Lump-Sum Formula A more general formulation… 𝑃𝑃 1 + 𝑖 𝑛 = 𝐹𝑃 PV is the Present Value (think of this as the beginning amount) FV is the Future Value (think of this as the ending amount) i = interest rate (or, return) per period n = number of periods over which the investment takes place FIN 300 - TVM Lump Sum 6
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Lump-Sum Formula We call this a “lump-sum” problem because no other money flows in to or out of the account, either after the initial investment or before we calculate the ending balance in the account – in other words, one single lump- sum is invested and stays put (is re-invested) in the account until the end FIN 300 - TVM Lump Sum 7
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Compound Interest Example Back to our previous example Plug into the formula… 𝑃𝑃 1 + 𝑖 𝑛 = 𝐹𝑃 $100 1 + 0.1 2 = $121 or $100(1.1)(1.1) = $110(1.1) = $121 FIN 300 - TVM Lump Sum 8
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Compounding We are moving forward in time , so we refer to this as compounding FIN 300 - TVM Lump Sum 9 T=0 T=1 T=2 Invest $100 (negative cash- flow) Cash Out $121 (positive cash-flow) Compounding Forward in Time
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