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Future Value: The value at a future date of dollar today

Future Value: The value at a future date of dollar today. Period 0 Period 1 Period 2 $1 $1*(1+r) {$1*(1+r)}*(1+r) $1*(1+r) 2 Rate of time preference : proportional increase in income required next period to compensate for the loss of $1 today :personal interest rate

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Future Value: The value at a future date of dollar today

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  1. Future Value: The value at a future date of dollar today Period 0 Period 1 Period 2 $1 $1*(1+r) {$1*(1+r)}*(1+r) $1*(1+r)2 Rate of time preference : proportional increase in income required next period to compensate for the loss of $1 today :personal interest rate Compounding: sequential computation of future value

  2. Future Value: The value at a future date of dollar today Period 0 Period 1 Period 2 Period 3 Period T $1 $1*(1+r) $1*(1+r)2 $1*(1+r)3 $1(1+r)T r = 0.10; T=40 $1 $1*(1.1) $1*(1.1)2 $1*(1.1)3 $1(1.1)40 $1 $1.10 $1.21 $1.33 $45.26

  3. Future Value: The value at a future date of dollar today Period 0 Period 1 Period 2 Period 3 Period T $1 $1*(1+r) $1*(1+r)2 $1*(1+r)3 $1(1+r)T r = 0.10; T=40 $1 $1*(1.1) $1*(1.1)2 $1*(1.1)3 $1(1.1)40 $1 $1.10 $1.21 $1.33 $45.26

  4. Present Value: The current value of a stream of future income Period 0 Period 1 $1 $1*(1+r) $1/(1+r) $1

  5. Present Value: The current value of a stream of future income Period 0 Period 1 Period 2 $1 $1*(1+r) $1*(1+r)2 $1/(1+r)2 $1/(1+r) $1 r = 0.1 $1/(1.1)2 $1/(1.1) $1 $0.83 $0.91 $1

  6. Present Value: The current value of a stream of future income Period 0 Period 1 Period 2 Period 3 Period T $1 $1*(1+r) $1*(1+r)2 $1*(1+r)3 $1(1+r)T $1/(1+r)T$1 r = 0.10; T=40 $1/(1.1)40$1 $0.022 $1

  7. Present Value: The current value of a stream of future income Stream of $1 every year for T periods, starting next period T Σ 1/(1+r)t = $1/(1+r) + $1/(1+r)2 + $1/(1+r)3 + … + $1/(1+r)T < T t=1

  8. Present Value: The current value of a stream of future income Stream of $1 every year for T periods, starting next period T Σ 1/(1+r)t = $1/(1+r) + $1/(1+r)2 + $1/(1+r)3 + … + $1/(1+r)T < T t=1 If r = 0.1; T = 40; Present Value = $9.78 If r = 0.05; T=40; Present Value = $17.16

  9. Present Value: The current value of a stream of future income $2000 furnace saves $200/year Good deal?

  10. Present Value: The current value of a stream of future income T Σ 1/(1+r)t t=1 $2000 furnace saves $200/year Good deal? If r = 0.1; T = 40; Present Value = $1956 Breakeven: NEVER If r = 0.05; T=40; Present Value = $3432 Breakeven: 15 years

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