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 correctly represents the future value of an ordinary annuity with periodic deposits of $P$, interest rate $r$ per period, and $n$ periods?

$FV = P \times \dfrac{(1 + r)^n - 1}{r}$

$FV = P \times (1 + r)^n$

$FV = P \times n \times r$

$FV = P \times \dfrac{1 - (1 + r)^{-n}}{r}$

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Verified step by step guidance

Step 1: Understand the concept of an ordinary annuity. An ordinary annuity involves periodic payments or deposits made at the end of each period, and the future value represents the accumulated amount after all payments and interest have been applied.

Step 2: Analyze the formula for the future value of an ordinary annuity. The correct formula is: FV = P × ( (1 + r)^n - 1 ) / r. This formula accounts for the compounding effect of interest over multiple periods.

Step 3: Compare the given formulas. The first formula matches the correct formula for the future value of an ordinary annuity, as it includes the periodic deposit amount (P), the interest rate per period (r), and the number of periods (n), along with the compounding effect.

Step 4: Evaluate why the other formulas are incorrect. For example: FV = P × (1 + r)^n represents the future value of a single lump sum, not an annuity. FV = P × n × r does not account for compounding interest. FV = P × (1 - (1 + r)^-n) / r represents the present value of an ordinary annuity, not the future value.

Step 5: Conclude that the correct formula for the future value of an ordinary annuity is FV = P × ( (1 + r)^n - 1 ) / r, as it properly incorporates periodic deposits, compounding interest, and the number of periods.