Present Value (PV) and Future Value (FV) are key to the concept of time value of money. PV and FV are related, which reflects compounding interest. Since it’s really rare to use simple interest, this formula is the important one. PV and FV vary directly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant.

The future value (FV) measures the nominal future sum of money that a given sum of money is “worth” at a specified time in the future assuming a certain interest rate, or more generally, rate of return. The FV is calculated by multiplying the present value by the accumulation function. The value does not include corrections for inflation or other factors that affect the true value of money in the future. The process of finding the FV is often called capitalization.

On the other hand, the present value (PV) is the value on a given date of a payment or series of payments made at other times. The process of finding the PV from the FV is called discounting .

The interest rate (or discount rate) and the number of periods are the two other variables that affect the FV and PV. The higher the interest rate, the lower the PV and the higher the FV. The same relationships apply for the number of periods. The more time that passes, or the more interest accrued per period, the higher the FV will be if the PV is constant, and vice versa.

The discount rate is the rate in which future cashflows are discounted to adjust for financial factors such as inflation and interest. This variable can also be the rate of return required by investors when considering a project for investment. In the FV formula, this is the compounding rate.

The time to maturity is the number of periods, often expressed in years, that a project or investment will run before reaching maturity, being retired, or sold.

Present value is nothing but how much future sum of money worth today. It is one of the important concepts in finance and it is a basis for stock pricing, bond pricing, financial modelling, banking, and insurance, etc. Present value provides us with an estimated amount to be spent today to have an investment worth a certain amount of money at a specific point in the future.

Future Value is the amount of money which will grow over a period of time with simple or compounded interest. It is one of the most important concepts of finance and it is based on the time value of money.

The calculation of present and future values of investments are important valuation concepts. For the following application examples, we will examine two different examples and calculate both present value of an investment based on set variables and then the future value of an investment using another set of variables.

Assume you are wanting to earn $20,000 from an investment in 5 years that has an interest rate or rate of return of 6%. You want to know the value to invest now, the present value, in order to earn the $20,000 from that investment. Using the present value formula, the present value of that investment can be calculated as follow:

PV = FV / (1+r)^{t}

PV = 20,000 / (1+0.06)^{5}

PV = $14,945.16

Using the Present Value formula, an investment that will yield $20,000 in 5 years’ time with a rate of return of 6% will have a present value of $14,945.16.

Now assume you want to invest $20,000 into a project that has a rate of return of 6% and a time to maturity of 5 years. You want to know the future value of that investment based on the present value and other variables. The formula for calculating the future value is as follows:

FV = PV * (1+r)^{t}

FV = 20,000 * (1+0.06)^{5}

FV = $26,764.51

Using the Future Value formula, the project will yield a future value of $26,764.51 in 5 years. This value can be used by the investor to compare other investments with different yields to determine which decision would be most beneficial to their future profits.

The advantages of the present and future value of investment are numerous. Present and future value are fundamental to the concept of the time value of money, the very cornerstone of valuation and investment practices. Calculating the present value of an investment using a discount rate allows investors to get an idea of what an investment will be worth in the future in present dollars. It allows investors to compare options and consider opportunity costs; the foregone investment opportunities in favour of what other investments they choose, all based around the valuation of principles of the time value of money. Future values allow investors to account for compounding and interest and inflation when considering investments. We cannot stress enough how important and advantageous Present and Future Values are. It is the basis of this entire platform.

The present value and future value of investments are integral to the concept of the time value of money. The value of the money you have now is not the same as it will be in the future. Knowing how to determine time value of money by calculating present and future value can help you distinguish between the worth of investments that offer returns at different times. It is integral to the very concept of valuation.

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- See Also:
- FV Annuity,
- Perpetuities,
- PV Annuity,