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# ch.9 - Ch.9 The basic tools of finance Definition of...

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Ch.9 The basic tools of finance Definition of finance: the field that studies how people make decision regarding the allocation of resources over time and the handling of financial risk. Measuring the time value of money Having money in your pocket today is more valuable having the same amount in your pocket in the future. For example, I would very much rather have 10 000\$ today than in 10 years. However, would I prefer 10 000\$ today or 15 000\$ in 10 years? Not clear. Prefer 10 000\$ because I could then lend the money at a 0.05 rate and get 16 300\$ five years from now. What if the prevailing rate is 4%? PV= 10 133.46\$. therefore I should prefer to take the 15 000 now. The point is that economists need tools to compare the value of money over time. Future Value Suppose you put Y dollars in the bank today at an interest rate “r” (e.g., r=0.05). Assume no tax. Suppose that interest is paid annually and that the interest – a process called compounding. Question: What is the future value (FV) of Y after N years? After 1 year: Y + rY = Y(1+r) After 2 years: Y(1+r)+ rY(1+r)= Y(1+r)(1+)= Y(1+r) 2 After 3 years: Y(1+r) 2 + r Y(1+r) 2 = Y(1+r) 2 (1+r) = Y(1+r) 3 So if the prevailing interest is r, the value of Y dollars N years from now is: FN= Y(1+r) N Present Value PV refers to the amount of money today that would be needed to produce using prevailing interest rates, a given future amount of money. PV= FV/ (1+r) N Compounding factor or PV= FV (1/(1+r) N Discounting factor Question: What is the PV of 15 000\$ in 10 years if the prevailing interest rate is 5%? PV= FV/(1+r) N = 15 000/ (1.05) 10 = 9 803.92\$ The concept of present value demonstrates the following: 1. Receiving a given sum of money in the present is preferred to receiving the same sum in the future.

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