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

Approximately what annual interest rate, compounded annually, is needed to double an investment over eight years?

12%

6.5%

8.7%

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Verified step by step guidance

Step 1: Understand the problem. The goal is to determine the annual interest rate required to double an investment over eight years using the formula for compound interest. The formula is: \( A = P(1 + r)^t \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years.

Step 2: Set up the equation based on the problem. Since the investment needs to double, \( A = 2P \). Substitute \( A = 2P \), \( t = 8 \), and \( P \) into the formula: \( 2P = P(1 + r)^8 \).

Step 3: Simplify the equation. Divide both sides of the equation by \( P \) (assuming \( P \neq 0 \)): \( 2 = (1 + r)^8 \).

Step 4: Solve for \( r \). Take the eighth root of both sides to isolate \( 1 + r \): \( 1 + r = \sqrt[8]{2} \). Then subtract 1 from both sides: \( r = \sqrt[8]{2} - 1 \).

Step 5: Interpret the result. The value of \( r \) represents the annual interest rate needed to double the investment over eight years. Use a calculator or logarithmic methods to approximate \( \sqrt[8]{2} \) if needed.