# The Time Value of Money

3/4/2019 Jacob Reed

A few years ago, the time value of money was added to the Advanced Placement (AP) macroeconomics exam. As an AP Economics teacher, I struggled to figure out how much detail my students needed to know about this topic for the AP Exam. Below you will find what I expect my students to know so they are prepared for exam day.

**What is the time value of money?**

The time value of money is the idea that money today will be worth more in the future given the interest rate that can be earned if the money is saved rather than spent. If a consumer saves $100 and earns 5% interest on that savings, the consumer will have $105 in one year’s time. So, the value of today’s $100 is $105 one year from now. This example, as exam questions are likely to be, is assuming no inflation.

**How to calculate the future value of money:**

To calculate the future value of money, use the following formula: dollars x (1 + interest – inflation). If you have $150 and could earn 10% interest but inflation will be 5%, the value of the $150 will be $157.50 one year from now. $150 x (1 + .10 – .05) = $157.50. Most questions will likely assume there is zero inflation or will ask for nominal values. If that is the case, dollars x (1 + interest) is all you need.

**How to calculate the present value of money: **

The same concept works in reverse; money received a year from now will have less value today. To calculate the present value of future money, use the formula: Dollars / (1 + interest – inflation). If you will be given $105 a year from now while the interest rate is 10% and inflation is 5%, the value of $105 received a year from now is just $100 today. $105 / (1 + .10 – .05) = $100. Just like future value questions, I expect most questions will assume there is zero inflation or will ask for nominal values. If that is the case, dollars / (1-interest) is all you need.

If you are taking the AP Macroeconomics exam you cannot use calculators, so you may want to use an approximate formula for present value. The approximate formula is present value ≈ future value – (future value x interest rate). So if the interest rate is 5% and the present value of $200 received a year from now would be approximately $190 ($200 – (200 x .05)).

**Which is more valuable?**

I expect students could see questions that combine future and present value; perhaps a question that asks students which of two amounts of money in two periods of time is more valuable. For example, if you are offered $100 today or $120 a year from now when the interest rate is 20% and inflation is 5%, which is a better deal? To answer a question like this, you can either calculate the present value of the $120 a year from now, or calculate the future value of $100. The future value of the $100 would be $115. $100 x (1 + .20 – .05) = $115). Since $120>$115, the $120 a year from now is a better deal. Given these numbers, the calculating the present value of $120 a year from now would be difficult without a calculator. It is $104.35. $120 x (1 + .20 – .05) = $104.35. Since $104>$100, taking the $120 a year from now has more present value and is therefore a better deal.

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