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 future value ($FV$) of a single sum invested today ($PV$) for $n$ periods at an annual interest rate $r$, with interest compounded once per period?

$FV = PV \times (1 - r)^n$

$FV = PV \div (1 + r)^n$

$FV = PV \times r \times n$

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

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Verified step by step guidance

Step 1: Understand the concept of future value (FV). Future value represents the amount of money an investment will grow to over time, given a specific interest rate and compounding period.

Step 2: Recognize the formula for future value with compound interest. The correct formula is $FV = PV \times (1 + r)^n$, where $PV$ is the present value, $r$ is the annual interest rate, and $n$ is the number of compounding periods.

Step 3: Analyze why the other formulas are incorrect. For example, $FV = PV \times (1 - r)^n$ incorrectly subtracts the interest rate, which does not reflect growth. Similarly, $FV = PV \div (1 + r)^n$ represents a discounting formula, not compounding. Lastly, $FV = PV \times r \times n$ assumes simple interest, not compound interest.

Step 4: Break down the correct formula. The term $(1 + r)^n$ accounts for compounding, where the investment grows exponentially over $n$ periods. Multiplying this by $PV$ scales the growth to the initial investment amount.

Step 5: Apply the formula to solve problems. To calculate future value, substitute the given values for $PV$, $r$, and $n$ into the formula $FV = PV \times (1 + r)^n$ and compute the result.