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Commerce 2FA3.docx

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Dr.Richard Deeves

Commerce 2FA3: Chapter 2 – Time Value 1. Present values and future values 2. Multiple cashflows 3. Annuities and perpetuities 4. Amortized loans Fibonacci and his friend Marco • Fibonacci was an Italian mathematician, living in middle ages in Pisa • His friend Marco (who didn’t relish working) had a sum of money and he wanted to know how long it would last given his spending rate (after which he would have to work). • His friend had 1000 florins. Spending 1/x of this amount per year, Marco’s money would run out in x years. • But banking was being developed in this part of Italy at the time and his friend wisely had his funds deposited in a Pisan bank that paid 20% interest/year Let’s think it through.. • Say he spent 300 fls/year • Year 1: IN: 200 OUT: 300 BALANCE: 900 • Year 2: IN: 180 (20% of 900) OUT: 300 BALANCE: 780 • Fibonacci thought long and hard about this Present value and time lines (2.1) V 0 V /11+k) (2.2) V 0 V /21+k) 2 (2.3) V 0 V/(t+k) t (2.4) V 0 V *tPVIF(k;t) Reversing direction and future value (2.3) V 0 V/(t+k) t (2.5) V t V *0(1+k) = V * F0IF(k;t) Using time value of money formulas (k = 10%) • PV of $500 received
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