What Is the Time Value of Money (TVM)?

The time value of money (TVM) surmises that money invested is worth more than its present value. TVM calculates the 澳洲幸运5官方开奖结果体彩网:future value of a sum of money, as💙suming the cash can grow over time and earn a positive ret🧔urn. 

Power of Compound Interest

A sum of money, once invested, can grow over time. Money deposited into a high-yield savings account will earn interest. Over the ensuing months and years, that interest will be added to the principal, earning more interest. That's what's known as the 澳洲幸运5官方开奖结果体彩网:power of compound interest. 

Money not invested can lose value over time. Hiding $1,000 in a mattress for three years will not only incur a loss of any additional money that could have been earned by investing it, but it will also have even less 澳洲幸运5官方开奖结果体彩网:buying power than it once did because 澳洲幸运5官方开奖结果体彩网:inflation will have reduced its value.

Time Value of Money Formula

The basic timꦦe value of money formula doesn't calculate "TVM" itself. Instead, it shows the change in the value of money over time. It calculates the future value of a sum of mone🎶y based on:

• Its present value
• Interest rate
• Number of compounding periods per year
• Number of years

澳洲幸运5官方开奖结♊果体彩网:Based on these variables, t🍌he TVM formula is:

$\begin{aligned}&FV = PV \Big ( 1 + \frac {i}{n} \Big ) ^ {n \times t} \\&\textbf{where:} \\&FV = \text{Future value of money} \\&PV = \text{Present value of money} \\&i = \text{Interest rate} \\&n = \text{Number of compounding periods per year} \\&t = \text{Number of years}\end{aligned}$​FV=PV(1+ni​)n×twhere:FV=Future value of moneyPV=Present value of moneyi=Interest raten=Number of compounding 💦periods per yeart=Number of years​

Investors can see the difference between the future value and the present value. The TVM formula may change slightly depending on the situation. For example, in the case of annuity or perpetuity payments, the generalized form🌠ula will have additional or fewer💫 factors.

Example

Assume a sum of $10,000 is invꦛested for one year at 10% interest compounded annually. The future value o🌸f that money is:

$\begin{aligned}FV &= \$10,000 \times \Big ( 1 + \frac{10\%}{1} \Big ) ^ {1 \times 1} \\ &= \$11,000 \\\end{aligned}$FV​=$10,000×(1+110%​)1×1=$11,000​

The formula can also be rearranged to find the value of the future sum in present-day dollars. For example, the present-day dol🐠lar amount compounded annually at 7% interest that would be worth $5,000 one year from today is:

$\begin{aligned}PV &= \Big [ \frac{ \$5,000 }{ \big (1 + \frac {7\%}{1} \big ) } \Big ] ^ {1 \times 1} \\&= \$4,673 \\\end{aligned}$PV​=[(1+17%​)$5,000​]1×1=$4,673​

Effects of Compounding Periods on FV

The number of compounding periods has a dramatic effect on the TVM calculations. Taking the $10,000 example above, if the number of compounding periods is increased to quarterly, 🌳monthly, or daily, the ending future value calculations are:

• Quarterly Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 4 } \Big ) ^ {4 \times 1} = \$11,038$FV=$10,000×(1+410%​)4×1=$11,038
• Monthly Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 12 } \Big ) ^ {12 \times 1} = \$11,047$FV=$10,000×(1+1210%​)12×1=$11,047
• Daily Compounding: $FV = \$10,000 \times \Big ( 1 + \frac { 10\% }{ 365 } \Big ) ^ {365 \times 1} = \$11,052$FV=$10,000×(1+36510%​)365×1=$11,052

This shows that the TVM depends not only on the interest rate and time horizon but also on&ꦿnbsp;how many times the compounding calculations are computed each year.

The Bottom Line

The future value of money isn't the same as present-day dollars. And the same is true about money from the past. This phenomenon is known as the time value of money (TVM). Both businesses and individuals can use the concept to make smart investment decisions.