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 $15,000 invested at an annual interest rate of 15% compounded annually for 5 years?

FV = 15{,}000 \times (1 - 0.15)^5

FV = 15{,}000 \times (1 + 0.15 \times 5)

FV = 15{,}000 \times (1 + 0.15)^5

FV = 15{,}000 \div (1 + 0.15)^5

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Verified step by step guidance

Step 1: Understand the concept of future value (FV). Future value is the value of an investment at a specific date in the future, calculated using the principle of compounding interest. The formula for FV with annual compounding is FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years.

Step 2: Identify the given values in the problem. The present value (PV) is $15,000, the annual interest rate (r) is 15% (or 0.15 in decimal form), and the number of years (n) is 5.

Step 3: Analyze the provided equations. The correct formula for FV with annual compounding is FV = PV × (1 + r)^n. This matches the equation FV = 15,000 × (1 + 0.15)^5. The other equations provided do not correctly apply the compounding formula.

Step 4: Substitute the given values into the correct formula. Replace PV with 15,000, r with 0.15, and n with 5 in the formula FV = PV × (1 + r)^n. The equation becomes FV = 15,000 × (1 + 0.15)^5.

Step 5: Explain why the other equations are incorrect. FV = 15,000 × (1 - 0.15)^5 incorrectly uses subtraction instead of addition, FV = 15,000 × (1 + 0.15 × 5) assumes simple interest rather than compounding, and FV = 15,000 ÷ (1 + 0.15)^5 incorrectly divides instead of multiplying.