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

If Ida invests $10 at an annual interest rate of 7% compounded annually, approximately how many years will it take for her investment to double?

About 5 years

About 20 years

About 10 years

About 14 years

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Verified step by step guidance

Step 1: Understand the problem. Ida wants to know how many years it will take for her investment to double at an annual interest rate of 7% compounded annually. This involves using the formula for compound interest and solving for time.

Step 2: Recall the compound interest formula: $ 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 3: Set $ A = 2P $ because the investment needs to double. Substitute $ P = 10 $, $ r = 0.07 $, and $ A = 20 $ into the formula: $ 20 = 10(1 + 0.07)^t $. Simplify to $ 2 = (1.07)^t $.

Step 4: Solve for $ t $ using logarithms. Take the natural logarithm (ln) of both sides: $ \ln(2) = t \cdot \ln(1.07) $. Rearrange to isolate $ t $: $ t = \frac{\ln(2)}{\ln(1.07)} $.

Step 5: Calculate $ \ln(2) $ and $ \ln(1.07) $ using a calculator, then divide $ \ln(2) $ by $ \ln(1.07) $ to find the approximate value of $ t $. This will give the number of years it takes for the investment to double.