Time Value of Money

Present versus Future Value of Money

Future Value of Money

Making sound investment decisions depends on a strong understanding of the future value of money.
Investors consider both future value and present value when making time value of money calculations. Future value (FV) is the measure of what an investment made today will be worth in the future, given number of periods, interest rate, and amount invested. Present value (PV) is the value in current dollars of a future payment discounted to the present. In other words, the future value is what a cash flow will be worth later, and the present value is what it is worth today. For example, if a bank is offering a certificate of deposit (CD) for investment over two years at 8 percent annual compounding interest, then an initial $1,000 investment will be multiplied by 1.08 at the end of the first year to get $1,080, which is what the investment would be worth at the end of year one. That amount would subsequently be multiplied again by 1.08 at the end of year two to come up with the compounding interest total of the investment, which would be $1,166.40 in total value after two years. Calculating present value as a reverse mathematical equation could also be completed.
PV=FV(1+r)n\text{PV}=\frac{\text{FV}}{(1+r)^n}
Where:
PV=Present ValueFV=Future Valuer=Interest Raten=Time Period\begin{aligned}\text{PV}&=\text{Present Value}\\\text{FV}&=\text{Future Value}\\ r&=\text{Interest Rate}\\ n&= \text{Time Period}\end{aligned}
Year One:
PV=$1,080(1+0.08)1=$1,000\begin{aligned}\text{PV}&=\frac{\$1{,}080}{(1\;+\;0.08)^1}\\\\&=\$1{,}000\end{aligned}
Year Two:
PV=$1,166.40(1+0.08)2=$1,000\begin{aligned}\text{PV}&=\frac{\$1{,}166.40}{(1\;+\;0.08)^2}\\\\&=\$1{,}000\end{aligned}
Based on these calculations, $1,166.40 in two years is worth the same as $1,000 in today's dollars if the interest rate is 8 percent. The future value of a present value sum, $1,080, with an interest rate of 8 percent for one and two years can be calculated using the future value of money formula.
FV=PV(1+r)n\text{FV}=\text{PV}\;(1+r)^n
Where:
FV=Future ValuePV=Present Valuer=Interest Raten=Time Period\begin{aligned}\text{FV}&=\text{Future Value}\\\text{PV}&=\text{Present Value}\\r&=\text{Interest Rate}\\n&=\text{Time Period}\end{aligned}
FV=$1,080(1+0.08)1=$1,166.40\begin{aligned}\text{FV}&=\$1{,}080\;(1+0.08)^1\\\\&=\$1{,}166.40\end{aligned}
FV=$1,166.40(1+0.08)2=$1,360.49\begin{aligned}\text{FV}&=\$1{,}166.40\;(1+0.08)^2\\\\&=\$1{,}360.49\end{aligned}
Thus, within the future value formula, the present value is required, and after one year at 8 percent interest, $1,080 grows to be $1,166.40 and after two years $1,080 grows to be $1,360.49.

For investors, knowing the future and present values of investment options can help determine investment decisions. Investors balance investment earning potential against the expected inflation rate (over the investment period) as well as the potential return other investments might bring. Investors balance risk with the potential reward as well. Some investments, such as government bonds, produce low returns, perhaps even lower than the rate of inflation, but they are very safe investments because they have low risk. Buying stock in an individual company, however, has the potential for a much higher return but comes at the price of much more risk. This risk may include the possibility of losing the investment in part or in full. Generally, the riskier the investment, the higher the return expected. The risk must be worthwhile to the investor.

The rule of 72 is a mathematical shortcut that investors can use when calculating the potential return on an investment. The rule is a simple formula in which 72 is divided by the compound annual interest rate. This calculation helps determine approximately how long it will take for an initial investment to double. For example, if Mary Nelson invests $1,000 earning 12 percent interest each year compounding annually, it will take approximately six years, 72/12=672/12=6, for Mary to double the initial investment from $1,000 to $2,000.

Impact of Compound Interest

The rule of 72, a mathematical formula shortcut, along with knowledge of the compound interest rate, can give a rough idea of how long it will take to double an investment. An initial investment of $1,000 will nearly double in value in approximately six years.

Future and Present Value of Money and Investment Decision-Making

Understanding the comparison between present and future values of money using mathematical tools is central to investment decision-making.

For consumers, time value of money considerations are relevant with regard to both investing and borrowing. Usury, or predatory lending, is the act of lending money to a borrower at an illegal and excessively high rate of interest. Lenders who make such loans are often referred to as loan sharks or payday lenders. Many states have laws limiting how high the interest rate on a loan can be. States also require lenders to state loans in terms of the annual percentage rate (APR) so borrowers know the cost of taking out a loan, but if the loan does not compound annually, using APR can misstate the actual cost of borrowing the funds. Thus, the effective annual rate is used to determine the annual effective yield of a loan. The effective annual rate (EAR) is a measurement of the annual compound interest rate when compounding occurs more than once a year.

For example, if Mary Nelson is carrying a balance on a credit card of $1,000 and the APR on the credit card is 24 percent compounded monthly, the balance owed of $1,000 on January 1 would be $1,020 on February 1 after the 2 percent monthly interest rate is added (24/12=224/12=2). Then, if Mary does not pay the credit card off right away, the following month more interest will accrue, not just on the initial debt but on the unpaid interest charges from prior months as well. Thus, the EAR will always be higher than the APR if the interest compounds more often than annually. Consumers need to take this into consideration if they are carrying any debts.

For many investors, if the EAR is high enough it may make more sense to pay down debt rather than investing in a new opportunity. It would depend on what the expected return of that investment might be. Paying off a debt at a high rate that compounds frequently does provide a guaranteed return on investment equal to the rate applied to the carried debt.

A small business may make a similar calculation when it comes to investing in the business. For example, Cogs Inc. wants to spend $25,000 to replace an old machine. It can either borrow the money and pay the accruing debt off over time or save enough from its revenues each month and invest that in purchasing the new machine outright. A future value calculator can tell the company how much should be saved each month over what number of months in order to save $25,000. Cogs Inc. would then compare the cost to its borrowing costs and determine the best financial decision.