Table of contents

1. Introduction to Accounting1h 21m
2. Transaction Analysis1h 13m
3. Accrual Accounting Concepts2h 38m
4. Merchandising Operations2h 30m
5. Inventory1h 55m
6. Internal Controls and Reporting Cash1h 16m
7. Receivables and Investments3h 8m
8. Long Lived Assets5h 1m
9. Current Liabilities2h 19m
10. Time Value of Money1h 23m
- Time Value of Money Equations
  35m
- Using Time Value of Money Tables
  47m
11. Long Term Liabilities2h 45m
12. Stockholders' Equity2h 15m
13. Statement of Cash Flows2h 24m
14. Financial Statement Analysis5h 25m
15. GAAP vs IFRS56m

10. Time Value of Money

Time Value of Money Equations

Financial Accounting

10. Time Value of Money

Time Value of Money Equations

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Multiple Choice

Which of the following formulas would most likely represent the present value of an ordinary annuity factor, where $r$ is the interest rate per period and $n$ is the number of periods?

$\dfrac{1}{(1 + r)^n}$

$\dfrac{(1 + r)^n - 1}{r}$

$(1 + r)^n$

$\dfrac{1 - (1 + r)^{-n}}{r}$

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Verified step by step guidance

Step 1: Understand the concept of an ordinary annuity. An ordinary annuity is a series of equal payments made at the end of each period over a specified number of periods. The present value of an ordinary annuity represents the current worth of these future payments, discounted at a specific interest rate.

Step 2: Recall the formula for the present value of an ordinary annuity. The formula is derived by summing the present values of each individual payment in the series. The general formula is: $ PV = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} $, where $ C $ is the payment amount, $ r $ is the interest rate per period, and $ n $ is the number of periods.

Step 3: Simplify the summation formula into a compact expression. Using mathematical techniques, the summation can be expressed as $ PV = \frac{1 - (1 + r)^{-n}}{r} $. This formula accounts for the discounting effect of the interest rate over $ n $ periods.

Step 4: Compare the given options to the derived formula. The correct formula for the present value of an ordinary annuity factor is $ \frac{1 - (1 + r)^{-n}}{r} $, which matches the last option provided in the problem.

Step 5: Verify the reasoning. The other options do not represent the present value of an ordinary annuity factor. For example, $ \frac{1}{(1 + r)^n} $ represents the present value of a single payment made at the end of $ n $ periods, and $ \frac{(1 + r)^n - 1}{r} $ represents the future value of an ordinary annuity.