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 equations correctly computes the present value (PV) of a single future cash flow (FV) to be received in $n$ periods, discounted at an annual interest rate $r$?

PV = \dfrac{FV}{(1 + r)^n}

PV = FV \times (1 + r)^n

PV = \dfrac{FV}{r^n}

PV = FV \times r \times n

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Verified step by step guidance

Understand the concept of present value (PV): Present value is the current worth of a future cash flow, discounted at a specific interest rate over a certain number of periods. It helps determine how much a future amount is worth today.

Identify the correct formula for computing PV: The formula for PV of a single future cash flow (FV) is derived from the principle of discounting, which accounts for the time value of money. The correct formula is PV = FV / (1 + r)^n.

Break down the formula: In the formula PV = FV / (1 + r)^n, 'FV' represents the future value of the cash flow, 'r' is the annual interest rate (expressed as a decimal), and 'n' is the number of periods until the cash flow is received.

Compare the given options: Analyze each option provided in the problem. The correct formula is PV = FV / (1 + r)^n, as it properly accounts for the compounding effect of the interest rate over 'n' periods. The other options either incorrectly multiply or divide by factors that do not represent the time value of money.

Conclude the reasoning: The correct formula, PV = FV / (1 + r)^n, ensures that the future cash flow is appropriately discounted to reflect its present value. This formula is widely used in financial accounting and investment analysis.