Definition
The future worth (or value) of one per period is the value that a single monetary unit will accumulate to over a specified number of periods when compounded at a specific interest rate. It reflects the concept compounded in time value of money calculations and serves as a fundamental component for understanding personal and corporate finance, investments, and various financial instruments.
Formula
The future value \( F \) of an investment is calculated using the formula: \[ F = P (1 + i)^n \]
where:
- \( P \) is the principal amount (initial investment),
- \( i \) is the interest rate per period,
- \( n \) is the number of periods.
Example Scenarios
Single Period Investment:
If you invest $1 at an interest rate of 5% per period for 1 period, the future value is: \[ F = 1 \times (1 + 0.05)^1 = 1.05 \]
Multiple Periods Investment:
If you invest $1 at an interest rate of 5% per period for 3 periods, the future value is: \[ F = 1 \times (1 + 0.05)^3 = 1.157625 \]
Frequently Asked Questions
What is the ‘Future Worth’ of an investment?
The ‘Future Worth’ represents the amount of money an investment will accumulate over time, taking into account compound interest.
Is the ‘Future Worth’ the same as ‘Present Value’?
No, the ‘Present Value’ is the current worth of a future sum of money or stream of cash flows given a specified rate of return, discounting future cash flows to the present time.
How does compounding frequency affect the Future Worth?
The more frequently interest is compounded, the higher the future worth will be. Common compounding frequencies include annually, semi-annually, quarterly, and monthly.
Can Future Worth be negative?
In typical investment scenarios, future worth is not negative as it represents the accumulation of value. However, if the context involves withdrawals or losses exceeding gains, the net value could effectively be negative when accounting for those factors.
What does compounding per period mean?
Compounding per period means that interest is added to the principal balance at the end of each period, and future interest calculations include previously earned interest, leading to exponential growth.
Related Terms with Definitions
Present Value (PV):
The current value of a future sum of money or stream of cash flows given a specified rate of return.
Time Value of Money (TVM):
A concept that asserts money available now is worth more than the same amount in the future due to its potential earning capacity.
Compound Interest:
Interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from prior periods.
Discount Rate:
The interest rate used to discount future cash flows to their present value.
Online Resources
Suggested Books for Further Studies
- “Principles of Corporate Finance” by Richard A. Brealey, Stewart C. Myers, and Franklin Allen.
- “Fundamentals of Financial Management” by Eugene F. Brigham and Joel F. Houston.
- “Financial Management: Theory & Practice” by Eugene F. Brigham and Michael C. Ehrhardt.
Fundamentals of Future Worth (or Value) of One Per Period: Finance Basics Quiz
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