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 you deposit $1,000 into a savings account that earns 10\% annual interest compounded annually, how many years will it take for your investment to grow to $2,000?

Approximately 7.00 years

Exactly 10 years

Approximately 7.27 years

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Verified step by step guidance

Step 1: Understand the problem. You are tasked with finding the number of years it will take for an initial deposit of $1,000 to grow to $2,000 in a savings account that earns 10% annual interest compounded annually. This involves using the formula for compound interest.

Step 2: Recall the compound interest formula: $ A = P \cdot (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: Substitute the known values into the formula. Here, $ A = 2000 $, $ P = 1000 $, and $ r = 0.10 $. The equation becomes $ 2000 = 1000 \cdot (1 + 0.10)^t $.

Step 4: Simplify the equation to isolate $ t $. Divide both sides by $ 1000 $: $ 2 = (1.10)^t $. Then, take the natural logarithm (ln) of both sides to solve for $ t $: $ \ln(2) = t \cdot \ln(1.10) $.

Step 5: Rearrange the equation to solve for $ t $: $ t = \frac{\ln(2)}{\ln(1.10)} $. Use this formula to calculate the approximate number of years it will take for the investment to double.