Question

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%. 2a. You get the same prize but the choice changes to $5,000 now or $5,250 in three years. What do you do? 2b. You get the same prize but the choice changes to $5,000 now or $5,500 in three years. What do you do? 2c. Explain the time value of money using this scenario as an example.

Answer 1

Interest rate is 3%

Option of receiving $5000 at end of 3 years

PV = FV/(1+r)^n

=5000/(1.03)^3

=5000/1.092727

=4575.708$

Thus one should take $5000 now

now if one gets 5250 in 3 years then

PV = 5250/1.092727

=4804.494$

Still one should opt for 5000$ immediately

now if one gets 5500 in 3 years then

PV = 5500/1.092727

=5033.28

Thus one should choose 5500$ after 3 years

Here Concept of time value of money applies that the $ after one year is not worth as $ received today because of following
Dollar has interest earning capacity
Risk of not getting dollar in future
Inflation eats up value of $