BUS202: Principles of Finance

Calculating the present value ($PV$) is a matter of plugging $FV$, the interest rate, and the number of periods into an equation.

LEARNING OBJECTIVE

• Distinguish between the formula used for calculating present value with simple interest and the formula used for present value with compound interest

KEY TAKEAWAYS

Key Points

• The first step is to identify if the interest is simple or compound. Most of the time, it is compound.
• The interest rate and number of periods must have consistent units.
• The PV is what a future sum is worth today given a specific interest rate (often called a "discount rate").

Key Terms

• compound interest: Interest, as on a loan or a bank account, that is calculated on the total on the principal plus accumulated unpaid interest.
• simple interest: interest paid only on the principal.

Finding the present value ($PV$) of an amount of money is finding the amount of money today that is worth the same as an amount of money in the future, given a certain interest rate.

Calculating the present value ($PV$) of a single amount is a matter of combining all of the different parts we have already discussed. But first, you must determine whether the type of interest is simple or compound interest. If the interest is simple interest, you plug the numbers into the simple interest formula.

$F V=P V \cdot(1+r t)$

Simple Interest Formula: Simple interest is when interest is only paid on the amount you originally invested (the principal). You don’t earn interest on interest you previously earned.

If it is compound interest, you can rearrange the compound interest formula to calculate the present value.

$P V=\frac{F V}{(1+i)^{n}}$

Present Value Single Payment: Finding the PV is a matter of plugging in for the three other variables.

Inputs

• Future Value: The known value of the money at a declared point in the future.
• Interest Rate (Discount Rate): Represented as either $i$ or $r$. This is the percentage of interest paid each period.
• Number of periods: Represented as $n$ or $t$.

Once you know these three variables, you can plug them into the appropriate equation. If the problem doesn't say otherwise, it's safe to assume the interest compounds. If you happen to be using a program like Excel, the interest is compounded in the PV formula. Simple interest is pretty rare.

One area where there is often a mistake is in defining the number of periods and the interest rate. They have to have consistent units, which may require some work. For example, interest is often listed as $X$% per year. The problem may talk about finding the $PV$ 24 months before the $FV$, but the number of periods must be in years since the interest rate is listed per year. Therefore, $n = 2$. As long as the units are consistent, however, finding the $PV$ is done by plug-and-chug.