For you to understand the language of finance, you must understand several key terms. These terms include the following:

• Amortized loan: A loan paid off in equal installments composed of both principal and interest.
• Annuity: A series of equal payments; these payments are made at the end of a specific time period for a specified number of time periods (generally months or years).
• Compound annuity: An investment that involves depositing the same amount of money at the end of each year for a certain number of years and allowing the investment to grow.
• Compounding (annually, quarterly, daily, etc.): The number of periods during the year where interest is calculated. Compound interest is where interest is paid on previously earned interest, as well as on the principal. The shorter the compounding period, the higher the effective annual rate of interest.
• Effective interest rate: The actual rate (as opposed to the stated or nominal rate) that is received after the effects of compounding have been taken into account.
• Future value (FV): The value of an investment at some point in the future.
• Interest or discount rate: The stated rate that you will receive for investing at a specified compounding period for a specified period of time.
• Nominal return: The return on your investment before the impact of inflation or taxes is taken into account.
• Present value (PV): The current value (today’s value) of a future sum of money.
• Principal: The money that you have available to invest or save, or the stated amount on a bond or deposit instrument.
• Real return: The rate of return on an investment after the impact of inflation is accounted for. The formula for approximating the real return is the nominal return minus inflation. The exact formula is [(1+ nominal return)/ (1 + inflation)] –1. In this class, we will use the exact formula.
• Reinvesting: Taking money that you have earned on an investment and investing it again.
• Tax-adjusted return: The return on your investment after the impact of federal and state taxes has been taken into account.

Compounding

How will different compounding periods impact my investment and investment returns?

Compounding periods refer to the frequency with which interest is applied to your investment. Interest may be compounded daily, weekly, monthly, semiannually, or annually. A key relationship exists between time and interest rate. The shorter the compounding period, the higher the effective annual interest rate (the actual rate you are earning on your investment after taking the effect of compounding into account). For example, if interest is compounded daily, the investment will grow faster than if the interest is compounded monthly or annually.

The formula for calculating the effective interest rate (EIR) is as follows:

EIR = [(1 + (nominal return or APR/# periods))] ^{# periods}) -­1

Problem 1: Impact of Compounding

Let’s illustrate the effect of compounding and the effective interest rate. The following are examples of four investments with four different nominal returns. Which of these investments would you rather own?

• Investment A—12.0 percent annually
• Investment B—11.9 percent semiannually
• Investment C—11.8 percent quarterly
• Investment D—11.7 percent daily

To figure out which investment is best for you, you must determine the effective interest rate of each investment. Remember, the formula is [(1 + (nominal return/# periods))] ^{# periods}) -1.

• For Investment A, the effective rate would be (1+.12/1)¹ ­- 1, or 12.00 percent.
• For Investment B, the effective rate would be (1+.119/2) ² -­ 1, or 12.25 percent.
• For Investment C, the effective rate would be (1+.118/4) ⁴ ­- 1, or 12.33 percent.
• For Investment D, the effective rate would be (1+.117/365) ³⁶⁵ - ­1, or 12.41 percent.

Even though Investment D has the lowest nominal return, because of compounding, it has the highest effective interest rate. Investment D would be the best vehicle, assuming you were lending money at this rate. Compounding makes an important difference!