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 calculates the present value (PV) of a single future sum (FV) to be received in $n$ periods at an interest rate $r$ per period?

PV = FV - (FV \times r \times n)

PV = FV \times r \times n

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

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

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Verified step by step guidance

Step 1: Understand the concept of present value (PV). Present value is the current worth of a future sum of money or cash flow, discounted at a specific interest rate over a certain number of periods. It accounts for the time value of money, which states that money available today is worth more than the same amount in the future due to its earning potential.

Step 2: Identify the formula for calculating the present value of a single future sum (FV). The correct formula is: PV = FV / (1 + r)^n, where FV is the future value, r is the interest rate per period, and n is the number of periods.

Step 3: Break down the formula. The denominator (1 + r)^n represents the compounding factor, which adjusts the future value to account for the interest rate and the number of periods. Dividing the future value by this factor gives the present value.

Step 4: Compare the given equations. The first equation, PV = FV - (FV × r × n), incorrectly subtracts a simple interest calculation from FV, which does not account for compounding. The second equation, PV = FV × r × n, incorrectly multiplies FV by the interest rate and number of periods, which also does not account for compounding. The third equation, PV = FV × (1 + r)^n, incorrectly multiplies FV by the compounding factor instead of dividing by it.

Step 5: Conclude that the correct formula is PV = FV / (1 + r)^n, as it properly accounts for the time value of money and the compounding effect over n periods.