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MGT338H5 (6)

Time Value of Money

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University of Toronto Mississauga
Louis Florence

Class 3The Time Value of MoneySuppose market interest rates are 10yearThat means if you invest 1000 today in 1 year you will have 100011011001000 your original principal100 interest We could also ask what is the present value PV the value NOW of 1100 to be received in 1 year if market interest rates are 10year Answer PVX such that X1101100X11001101000What is the PV of 1000 in 1 year if the interest rate is 10 Answer X such that X1101000X100011090909 What would you rather have 90909 now or 1000 in 1 yearExample If interest rates are 12year what does 1500 grow to in 5 years In 1 year 1500150011216801500180 of interest In the second year 16801680112188160 Note 188160 150038160 and 180 x 2360 and 381603602160 2160 is the interest earned in the second year on the interest earned in the first yearBenjamin Franklin Money makes money and the money that money makes makes more money5In 5 years 15001500112150017623264351 We say 264351 is the future value FV of 1500 in 5 years if interest rates are 12 annually with annual Tcompounding In general FVC1rwhere C is the amount invested rthe annual 00rate and Tthe number of years it is invested for Similarly What is the PV of 264351 55in 5 years if r12 PVX such that X112264351X2643511121500PV of an amount C in 1 year PVC1r11TPV of an amount C in T years is PVC1rTTSuppose we invest C now in return for0C in 1 year1C in 2 years2C in T yearsTFirst note If r is the appropriate annual interest rate the PV of the future payments is 2Tgiven by PV C1rC1rC1r12T2TAnd the Net Present Value NPVCC1rC1rC1r012T
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