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Lecture1TVM.F11

# Lecture1TVM.F11 - Compound Interest Formulas The Time Value...

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9/23/11 1 The Time Value of Money C n : Future value at end of n periods of C 0 dollars tod r: Interest rate C 1 = C 0 + rC 0 (deposit C 0 for 1 period) C 1 = C 0 (1 + r) C 2 = C 1 + rC 1 (deposit C 1 for 1 period) C 2 = C 1 (1 + r) = C 0 (1 + r) 2 Recursively C n = C 0 (1 + r) n Compound Interest Formulas Example: \$100 at 5% for 5 years Year Beginning Amount Interest Ending 1 100 5 105 2 5.25 110.25 3 5.51 115.76 4 5.79 121.55 5 6.08 127.63 C 5 = 100(1.05) 5 = 100 × 1.2763 Simple vs. Compound Interest

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9/23/11 2 Doubling your money Let C n = 2C 0 n* = ln2/ln(1 + r) = .69315 ln(1 + r) Rule of 72: n* = 72 100r Rule of 69: n* = 0.35 + 69 100r Recommendation: Use your calculator! Rules of Time Travel with Money Only cash flows that occur at the same point in time can be compared To move a cash flow forward - compound Another example: Present Values/Discounting The present value of a payment of \$C, n periods from now is PV n (C) PV n (C) = C (1 + r ) n Since C 0 = C n + r ) n
9/23/11 3 Present Values/Discounting Present values are ADDITIVE PV(C 1 ,C 2 ,...,C n ) = PV 1 (C 1 ) + PV 2 (C 2 ) + . .. + PV n (C n ) = t = 1 n PV t (C t ) To move a cash flow backward - discount Example : Interest rate (%) PV(X) (\$) PV(Y) (\$) 0 1000 900 2 898 848 5 772 777 8 671 714 10 614 676 12 565 641 YOUR CHOICE DEPENDS ON THE INTEREST RATE

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Lecture1TVM.F11 - Compound Interest Formulas The Time Value...

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