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

How long (in years and months) will it take for an investment to double at an annual interest rate of 6\% compounded monthly?

Approximately 9 years and 6 months

Approximately 11 years and 8 months

Approximately 8 years

Exactly 12 years

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Verified step by step guidance

Step 1: Understand the formula for compound interest. The formula is \( A = P(1 + \frac{r}{n})^{nt} \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate, \( n \) is the number of compounding periods per year, and \( t \) is the time in years.

Step 2: Set \( A \) equal to \( 2P \) because the investment needs to double. Substitute \( r = 0.06 \) (6% annual interest rate) and \( n = 12 \) (monthly compounding) into the formula.

Step 3: Rearrange the formula to solve for \( t \). Divide both sides by \( P \), resulting in \( 2 = (1 + \frac{0.06}{12})^{12t} \). Take the natural logarithm (ln) of both sides to isolate \( t \).

Step 4: Use the logarithmic property \( \ln(a^b) = b \cdot \ln(a) \) to simplify. The equation becomes \( \ln(2) = 12t \cdot \ln(1 + \frac{0.06}{12}) \). Solve for \( t \) by dividing \( \ln(2) \) by \( 12 \cdot \ln(1 + \frac{0.06}{12}) \).

Step 5: Convert the value of \( t \) into years and months. Since \( t \) represents time in years, multiply the decimal portion of \( t \) by 12 to find the number of months.