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Finance
In this situation, the cost of the car is $25,000 and I have $10,000, meaning I am $15,000 short. The interest rate is 3%. The $5,000 that I have in cash will in three years be worth:
This will not be enough to purchase the car. However, collecting $5,000 three years instead of $5,000 today is absurd. The value of $5,000 in three years is going to be:
Thus, I would be giving away the difference either between this amount and $5,000 today, or the difference between $5,000 and $5,463.64 in the future.
As noted the value of $5,000 today, given three years at 3% interest, is $5,463.64. Thus, I would take $5,000 today and invest it, over taking $5,250 in three years' time.
Given that $5,000 invested today at 3% will be worth $5,463.64 in three years' time -- assuming annual compounding -- I would take $5,500 in three years' time over $5,000 today. The only reason I wouldn't is if I thought the interest rate was going to go up in that time. However, given a stable 3% rate, I would take $5,500 in three years' time.
1c. The time value of money reflects the fact that there is inflation and interest. The inflation rate and the interest rates are not the same, but both contribute to the change in the valuation of money over time. For example, over the next three years there will be inflation, and this inflation will reduce the buying power of that money....
We saw in this scenario that the car did not increase in price. If the rate of inflation was at 1%, for example, the car's price would have changed to $25,757. Thus, the person seeking to save $25,000 would still not have enough to buy the car.
The same holds true for interest. Because money can be invested, the time value of money in hand is the interest foregone, should you keep the money in cash. For example, if this $5,000 is kept in cash, then in three years it will still be worth $5,000. If it is invested at 3% compounding annually, then it will be worth $5,463.64. The time value of money is therefore $463.64 in income that would be lost by not investing that money.
For somebody seeking to minimize their losses, they must invest money so that the interest on that money covers the rate of inflation. This is why, even if the rate of inflation is low, the money needs to be invested rather than staying in cash. If there is any inflation at all, the cash will gradually lose value over time. This loss is what is referred to as the time value of money.
Overall, what I would do is to take the 5% and invest the money. There are other ways that the time value of money can play out in this scenario as well. For example, the interest paid when car companies offer financing is also an example of the time value of money at work. However, sometimes dealers will offer financing that is…
Works Cited:
Investopedia. (2012). Annual percentage rate. Investopedia.com. Retrieved June 19, 2012 from http://www.investopedia.com/terms/a/apr.asp#axzz1yHSMIRVt
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