Additional Detail on Present and Future Values
This section gives more detail on computing present and future values. It shows you how to compute more complex problems involving future and present values when there are multiple compounding periods and when the time duration of those problems are longer or are less than one year.
The Relationship Between Present and Future Value
Present value () and future value ( ) measure how much the value of money has changed over time.
Discuss the relationship between present value and future value
- The future value ( ) 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 is calculated by multiplying the present value by the accumulation function.
- and vary jointly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant.
- As the interest rate (discount rate) and number of periods increase, increases or decreases.
- discounting: The process of finding the present value using the discount rate.
- present value: a future amount of money that has been discounted to reflect its current value, as if it existed today
- capitalization: The process of finding the future value of a sum by evaluating the present value.
The future value () 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 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 is often called capitalization.
On the other hand, the present value () is the value on a given date of a payment or series of payments made at other times. The process of finding the from the is called discounting.
and are related , which reflects compounding interest (simple interest has multiplied by , instead of as the exponent). Since it's really rare to use simple interest, this formula is the important one.
FV of a single payment: The PV and FV are directly related.
and vary directly: when one increases, the other increases, assuming that the interest rate and number of periods remain constant.
The interest rate (or discount rate) and the number of periods are the two other variables that affect theand . The higher the interest rate, the lower the and the higher the . The same relationships apply for the number of periods. The more time that passes, or the more interest accrued per period, the higher the will be if the is constant, and vice versa.
The formula implicitly assumes that there is only a single payment. If there are multiple payments, theis the sum of the present values of each payment and the is the sum of the future values of each payment.
Source: Saylor Academy
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