FutureValue and CompoundOInterestFuture Value in two years$100+$100(0.05)+$100(0.05)+ $5(0.05)=$110.25Present Value of the Initial Investment+ Interest on the initial investment in the 1st Year+ Interest on the initial investment in the 2nd Year+ Interest on the Interest from the 1stYear in the2nd Year=Future Value in TwoYears4-6
4-6 Future Value and Compound Interest Future Value in two years $100+$100(0.05)+$100(0.05) + $5(0.05) =$110.25 Present Value of the Initial Investment + Interest on the initial investment in the 1st Year + Interest on the initial investment in the 2nd Year + Interest on the Interest from the 1stYear in the 2nd Year = Future Value in Two Years
Future Value and CompoundOInterestGeneral Formula-Futureyalueof aninvestment of PV in n years at interest ratei (measured as a decimal, or 5% = .05)FVn= PV*(1+i)r4-7
4-7 Future Value and Compound Interest General Formula – Future value of an investment of PV in n years at interest rate i (measured as a decimal, or 5% = .05) FVn = PV*(1+i)n
FutureeValueandCompound0InterestTable4.1Computing the FutureValue of S100 at 5%Annual InterestComputationFuture ValueYears into Future1$100(1.05)$105.002$100(1.05)2$110.253$100(1.05)3$115.764$100(1.05)4$121.555$100(1.05)5$127.63$100(1.05)1010$162.894-8
4-8 Future Value and Compound Interest Computing Future Value at 5% Annual Interest
Future Value and CompoundaInterestNote:Both n and i must be measured in sametime units-ifiis annual, then n must be inyears, So future value of $100 in 18months at 5% isFV = 100 *(1+.05)1.54-9
4-9 Future Value and Compound Interest Note: Both n and i must be measured in same time units—if i is annual, then n must be in years, So future value of $100 in 18 months at 5% is FV = 100 *(1+.05)1.5
4.2 Present ValueaPresent Value (PV) is the value today (inthe present) of a payment that is promisedto be made in the future.ORPresent Value is the amount that must beinvestedtodayinorderto realize a specifioamountona givenfuture date4-10
4-10 4.2 Present Value Present Value (PV) is the value today (in the present) of a payment that is promised to be made in the future. OR Present Value is the amount that must be invested today in order to realize a specific amount on a given future date