5 Steps to a 5 AP Macroeconomics 2019

Money, Banking, and Monetary Policy ❮ 143

useful, with essentially the same value, a week or a month later. If I were the town cheese

maker, I must quickly find merchants with whom to exchange my cheese, because if

I wait too long, moldy cheese loses its value.

Time Value of Money
Money may serve as a store of value, but money does lose its value over time. Most of us
prefer to receive money income as early as possible (the sooner we can begin to consume
stuff) and pay our debts as late as possible. If you lend your best friend $100, would you
rather be paid back tomorrow or five years from tomorrow? If you are not going to charge
your best friend any interest on this loan, then you probably prefer your money as soon as
possible. If your best friend paid you back in five years without interest, your $100 would
certainly have lost value over time due to inflation. After all, not having $100 for such a long
period of time means that you were unable to consume $100 worth of goods! Delaying your
consumption of goods that would give you utility must surely come at a cost. The idea of
a time value of money is perhaps the most important reason for paying interest on savings
and charging interest on borrowing.

Present Value and Future Value

Many decisions in life involve paying upfront costs today with the promise of a payoff
tomorrow or even years from now. Many of you are familiar with this trade-off because
you were told by a parent that “If you finish eating your vegetables, you can watch TV
before bedtime,” or “If you wash the car, you can go to the movie with your friends.” As
you consider attending college, the same principle applies. The costs (tuition, books, etc.)
are paid today, but the payoffs (marketable skills, useful knowledge, etc.) are received years
from today. As the previous section illustrates, dollars today are worth more than future
dollars; so there must be a way to convert present and future dollars to the same time period
so that wise decisions can be made. The interest rate is the key.
Let’s again assume that you are going to lend your friend $100 and that he is going
to pay you back in one year. We’ll also assume that there is no inflation, so a 10 percent
nominal interest rate is equal to the real interest rate. The opportunity cost of lending your
friend $100 is the interest you could have earned—$10, after a year had passed. So the
interest rate measures the cost to you of forgoing the use of that $100. After all, you could
have spent $100 on clothing right now that would have provided immediate benefit to you.
To see the relationship between dollars today (present value, or PV) and dollars one year
from now (future value, or FV), we can use a simple equation:

FV = PV × (1 + r)
or, using our example:

FV = $100 × (1.10) = $110

In other words, one year into the future, that $100 will be worth $110.
We can also rearrange our equation and solve for the present value PV:
PV = FV/(1 + r)
and, using our example again:

PV = $110/(1.10) = $100

This tells us that $110 a year from now is worth only $100 in today’s dollars.
If you were lending the money for a period of two years,
FV = PV(1 + r)^2 = $100 × (1.10) × (1.10) = $121