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BU111 Winter 2018 - Week #9 - Economic Factors - Time Value of Money - Student's Copy.ppt

# BU111 Winter 2018 - Week #9 - Economic Factors - Time Value of Money - Student's Copy.ppt

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BU111-S1 Winter 2018 Lecture #9 – Economic Factors Time Value of Money Lecturer: Brandon Van Dam

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Learning Objectives Describe the concept of time value of money Understand how to calculate and explain the Future Value and Present Value of single and multiple amounts with varying payment and interest periods
Time Value of Money Is \$1 one year from today worth the same as \$1 today? Answer: No it’s worth less because of - Risk - Real interest - inflation Concepts important to leases, mortgages, bonds, retirement contributions, stock valuation, project selection

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Single Amount – FV Single Period What will you have in one year if you deposit \$100 into an account today that earns 4% interest compounded annually? \$100 ? Today 1 104 \$ ) 04 . 1 ( 100 \$ amount single FV ) 1 ( amount single r PV FV X 1.04 \$104 r=.04 (interest or discount rate) PV = \$100 (single amount that is known today) n=1 (number of payment periods)
Single Amount – FV Multiple Periods What will you have in 3 years if you deposit a \$100 gift into an account today that earns 4% interest compounded annually? \$100 ? Today 1 r=.04 PV = \$100 n=3 49 . 112 \$ ) 04 . 1 ( 100 \$ 3 SA FV n r PV FV ) 1 ( SA 2 3 X 1.04= \$104 \$108.16 X 1.04= X 1.04= \$112.49

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Sample Problem How much money will you have in five years if you deposit \$200 into an account that earns 3% compounded annually? n SA r PV FV ) 1 (
Single Amount – PV Single Period How much do you have to deposit today to have \$100 after one year (assuming 4% interest compounded annually?) OR what is the present value of \$100 to be received in one year (assume a 4% discount rate).

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Single Amount – PV Single Period ? Today 1 r=.04 FV = \$100 ÷ 1.04 \$100 ) 1 ( amount single r FV PV 15 . 96 \$ ) 04 . 1 ( 100 \$ amount single PV \$96.15
Single Amount – PV Multiple Periods How much do you have to deposit today to have \$100 after three years (assuming 4% interest compounded annually?) OR what is the present value of \$100 to be received in three years (assume a 4% discount rate).

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Single Amount – PV Multiple Periods ? \$100 Today 1 r=.04 FV = \$100 n=3 2 3 PV single amount FV (1 r ) n 90 . 88 \$ ) 04 . 1 ( 100 \$ 3 amount single PV
Sample Problem How much do you have to deposit today to have \$3,000 four years from now (assume a 5% discount rate)? n r FV PV ) 1 ( SA

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Annuities Annuity: multiple but equal payments over equal periods of time Ordinary Annuity = payment does not start today Annuity Due = payment starts today
FV – Multiple Payments & Periods What will you have after three years if you deposit \$100 each year for three years (beginning at the end of this year) into an account that earns 4% interest compounded annually?

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FV – Multiple Payments & Periods \$100 Today 1 r=.04 PMT = \$100 n=3 2 3 \$100 X 1.04 ? 16 . 312 \$ 100 104 \$ 16 . 108 \$ OA FV =\$108.16 =\$104 r r PMT FV n 1 ) 1 ( annuity ordinary 04 .
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