Future Worth of One Per Period

Definition

The Future Worth of One Per Period (also referred to as Compound Amount of One Per Period) is a financial concept in real estate that calculates the future value of a series of equal periodic cash flows (annuities) when each payment is compounded at a specified interest rate. This metric helps investors and financial analysts in assessing the future value of consistent investments or series of payments over time.

Mathematically, the future worth can be calculated using the formula:

\[ F = PMT \times \frac{(1 + r)^n - 1}{r} \]

where:

$ F $ = Future Value
$ PMT $ = Periodic Payment
$ r $ = Interest Rate per Period
$ n $ = Number of Periods

Examples

Investment Scenario: Suppose you invest $1,000 at the end of each year for 5 years in an account that earns an annual interest rate of 5%. Using the above formula, you can calculate the future worth of these periodic investments.

\[ F = 1000 \times \frac{(1 + 0.05)^5 - 1}{0.05} = 1000 \times 5.52563 = 5525.63 \]

Thus, after 5 years, the future worth of these investments would be $5,525.63.
Mortgage Payments: Consider a scenario where a real estate investor makes annual mortgage payments of $2,000 at an interest rate of 4% for a term of 10 years. Calculating the future worth gives:

\[ F = 2000 \times \frac{(1 + 0.04)^{10} - 1}{0.04} = 2000 \times 12.006 = 24012 \]

The future worth of these mortgage payments after 10 years would be $24,012.

FAQs

What is the relation between Future Worth of One Per Period and Present Value of an Annuity?

While the Future Worth of One Per Period calculates the compounded future value of periodic payments, the Present Value of an Annuity calculates the present worth of those future payments. They are inverse concepts in terms of time value of money, with one looking forward and the other looking backward in time.

How is the Future Worth of One Per Period used in real estate investment?

In real estate investment, it is used to forecast the value of consistent cash flows from investment properties, evaluate mortgage payment schedules, and determine future investment values necessary for decision-making.

What factors affect the calculation of Future Worth of One Per Period?

Key factors include the periodic payment amount, interest rate per period, and the total number of periods. Changes in any of these elements can significantly affect the future worth.

Time Value of Money: The concept that money available now is worth more than the same amount in the future due to its potential earning capacity.
Compounding: The process of earning interest on both the initial principal and the accumulated interest from previous periods.
Annuity: A series of equal payments made at regular intervals over a specified period.

Online Resources

References

“Financial Management and Analysis,” Frank J. Fabozzi and Pamela P. Peterson.
“Real Estate Finance and Investments,” William Brueggeman and Jeffrey Fisher.
“Principles of Corporate Finance,” Richard A. Brealey, Stewart C. Myers, and Franklin Allen.

Suggested Books

“Time Value of Money and Discounting,” by Glen Arnold
“Real Estate Principles: A Value Approach,” by David C. Ling and Wayne R. Archer
“Investing in Real Estate,” by Gary W. Eldred

Future Worth of One Per Period Fundamentals Quiz

### What does the Future Worth of One Per Period represent? - [x] The future value of a series of equal periodic cash flows compounded at a specific rate. - [ ] The present value of a series of unequal cash flows. - [ ] The future value of a lump sum investment. - [ ] The present value of a perpetual annuity. > **Explanation:** The Future Worth of One Per Period calculates the accumulated value of uniform, periodic investments or payments, compounded at a specific interest rate over time. ### What is required to calculate the Future Worth of One Per Period? - [ ] Rate of inflation - [ x ] Interest rate per period - [ ] Rate of depreciation - [ ] Tax rate > **Explanation:** To calculate the Future Worth of One Per Period, you need the periodic payment amount, the interest rate per period, and the number of periods. ### In which scenarios is the Future Worth of One Per Period commonly used? - [x] Investment planning and mortgage payments - [ ] Evaluating one-time lump sum investments - [ ] Calculating property taxes - [ ] Asset amortization > **Explanation:** It is commonly used for scenarios involving series of periodic payments or investments, such as investment planning and mortgage payment calculations. ### Which formula is used for calculating the Future Worth of One Per Period? - [x] \$ F = PMT \times \frac{(1 + r)^n - 1}{r} \$ - [ ] \$ PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} \$ - [ ] \$ F = P \times (1 + r)^n \$ - [ ] \$ PMT = PV \times \frac{r}{1 - (1 + r)^{-n}} \$ > **Explanation:** The formula \$ F = PMT \times \frac{(1 + r)^n - 1}{r} \$ is specifically used for calculating the future worth of uniform periodic investments. ### What happens to the future worth if the interest rate increases, assuming all other factors remain constant? - [x] Future worth increases - [ ] Future worth decreases - [ ] Future worth remains unchanged - [ ] It depends on the payment amount > **Explanation:** An increase in the interest rate results in the periodic payments accruing more interest, thereby increasing the future worth. ### Is the Future Worth of One Per Period applicable for a series of varying payments? - [ ] Yes, it applies to any series of payments. - [ ] Yes, but only for mortgages. - [x] No, it is applicable only for uniform, periodic payments. - [ ] Yes, but only under special conditions. > **Explanation:** The future worth calculation is designed specifically for uniform, periodic payments and does not work correctly for variable payments. ### How does the number of periods (n) affect the Future Worth of One Per Period? - [x] Increasing the number of periods increases the future worth. - [ ] Changing the number of periods does not affect the future worth. - [ ] Increasing the number of periods decreases the future worth. - [ ] It has a variable impact depending on the payment amount. > **Explanation:** Increasing the number of periods allows the payments to compound for a longer duration, resulting in a higher future worth. ### For a given periodic payment and interest rate, what will a higher number of periods (higher n) result in? - [ ] Decreased future worth of other unrelated investments - [x] Higher future worth for the same investment - [ ] Higher inflation rate - [ ] Reduced periodic payments > **Explanation:** A higher number of periods will increase the amount of time over which the payments accrue interest, resulting in a higher future worth. ### What is the significance of "r" in the Future Worth of One Per Period formula? - [ ] It represents the periodic payment amount. - [x] It represents the interest rate per period. - [ ] It represents the total future value. - [ ] It represents the cumulative payment. > **Explanation:** "r" in the formula stands for the interest rate per period which is crucial in the compounding process. ### Why is understanding the Future Worth of One Per Period important in real estate investment? - [x] It helps in forecasting future values of investments. - [ ] It is used to determine immediate tax liabilities. - [ ] It benefits in negotiating rent agreements. - [ ] It assists in reducing property insurance costs. > **Explanation:** Understanding the Future Worth of One Per Period is essential for forecasting the accumulated value of investment or mortgage payments over time, aiding in better financial planning and decisions in real estate investment.

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