Future Worth (or Value) of One Per Period

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.

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

### What is the future value after 3 years with a $1 investment at an interest rate of 5% per period? - [ ] $1.05 - [ ] $1.15 - [x] $1.157625 - [ ] $1.105 > **Explanation:** Using the formula \$ FV = PV \times (1 + i)^n \$, where $PV = 1$, \$ i = 0.05 \$, and \$ n = 3 \$: \\[ FV = 1 \times (1.05)^3 = 1.157625 \\] ### Which formula is used to calculate the future value of an investment? - [x] \$F = P (1 + i)^n\$ - [ ] \$F = P / (1 + i)^n\$ - [ ] \$F = P (1 - i)^n\$ - [ ] \$F = P + (i \times n)\$ > **Explanation:** The future value is calculated using the compound interest formula \$ F = P (1 + i)^n \$. ### If the compounding interest rate is 6% annually, what will $1 grow to in 2 years? - [ ] $1.06 - [x] $1.1236 - [ ] $1.12 - [ ] $1.1366 > **Explanation:** Using the formula \$FV = PV \times (1 + i)^n\$: \\[ FV = 1 \times (1 + 0.06)^2 = 1.1236 \\] ### What does 'one per period' mean in the context of future worth? - [ ] Investing one unit every period - [x] One monetary unit invested initially for all periods - [ ] One unit added each period - [ ] One interest rate applied per period > **Explanation:** 'One per period' references a single monetary unit invested initially that compounds over the periods. ### Why is future worth important in finance? - [ ] It measures the reduction in financial value. - [x] It helps assess the growth potential of investments. - [ ] It calculates depreciation. - [ ] It estimates current investment performance. > **Explanation:** Future worth is essential for evaluating how investments grow over time with interest, aiding in financial planning and investment decisions. ### What effect does increasing the number of compounding periods have on future worth? - [x] Increases future worth - [ ] Decreases future worth - [ ] No effect - [ ] Initially increases then decreases > **Explanation:** Increasing the number of compounding periods results in interest being applied more frequently, which increases the future worth through compounding. ### How is future worth different from present value? - [ ] Future worth is discounted. - [x] Future worth considers interest over time, whereas present value discounts future cash flows to the present. - [ ] Future worth is always higher. - [ ] Present value does not consider time. > **Explanation:** Future worth indicates how much an investment grows over time, factoring in interest, while present value represents the current value of those future cash flows discounted back to present day. ### What is the key variable in determining the future worth of an investment? - [ ] Depreciation rate - [ ] Accounting method - [x] Interest rate - [ ] Tax rate > **Explanation:** The interest rate is a crucial variable in determining future worth as it governs the rate at which the investment grows. ### Can the future worth be lower than the initial investment? - [ ] Yes, always. - [ ] No, never. - [x] Yes, if the rate of return or compounding is negative. - [ ] It depends on the investment type. > **Explanation:** Future worth can be lower due to negative interest rates or losses, though typical positive compounding results in growth. ### Which of the following adjusts future worth calculation accuracy? - [x] Compounding frequency - [ ] Investment color - [ ] Transaction fees - [ ] Market conditions > **Explanation:** The frequency of compounding (annually, semi-annually, quarterly, etc.) directly affects the calculation of future worth, modifying how often interest is applied.

Thank you for expanding your understanding of future worth (or value) of one per period in finance! Continue exploring and mastering financial concepts.

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