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
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
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
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
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
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
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
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
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