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Time Value of Money: Present Value and Interest

You've been saving up for a new car that you think costs $25,000. You already have $10,000 and you think that, with interest and additional savings, the $10,000 will grow to $20,000 in three years. Suddenly, the phone rings and a voice at the other end of the line tells you that you've won $5,000. You have the choice of collecting the $5,000 immediately, or collecting it in three years which will give you enough money to buy the car. What would you do? Assume that the price of the car stays constant over the three years and that available interest for bank savings is 3%.

a) You get the same prize but the choice changes to $5,000 now or $5,250 in three years. What do you do?
b) You get the same prize but the choice changes to $5,000 now or $5,500 in three years. What do you do?
c) Explain the time value of money using this scenario as an example.

Solution Preview

Alternative 1
Collect the $5,000 immediately.
In this PV of this alternative =$5000

Alternative 2
Collect it in three years

Rate of interest =r=3%
Number of periods=n=3 years
FV of winning=FV=$5000
PV of winning=FV/(1+r)^n=5000/(1+3%)^3=$4575.71

PV of alternative 1 is higher. I should collect the money immediately.

a) You get the same prize but the choice changes to $5,000 now or $5,250 in three years. What do you do?

Alternative 1
Collect the $5,000 immediately.
In this PV of this alternative =$5000

Alternative ...

$2.19