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

To what amount will $P invested for n years at an annual interest rate of r percent, compounded annually, accumulate?

$P(1 + r)^n$

$P(1 + n)^r$

$P \times r \times n$

$P(1 + r \, n)$

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Verified step by step guidance

Step 1: Understand the concept of compound interest. Compound interest is calculated on the initial principal and also on the accumulated interest from previous periods. The formula for compound interest is: $ A = P(1 + r)^n $, where $ A $ is the accumulated amount, $ P $ is the principal, $ r $ is the annual interest rate (in decimal form), and $ n $ is the number of years.

Step 2: Analyze the given options. The correct formula for compound interest is $ P(1 + r)^n $. The other options provided do not correctly represent the compounding process. For example, $ P(1 + n)^r $ incorrectly applies the interest rate as an exponent to the time period, and $ P \times r \times n $ represents simple interest, not compound interest.

Step 3: Break down the correct formula $ P(1 + r)^n $. Here, $ (1 + r) $ represents the growth factor for one year, and raising it to the power of $ n $ accounts for compounding over $ n $ years.

Step 4: Convert the annual interest rate $ r $ from a percentage to a decimal by dividing it by 100. For example, if $ r $ is 5%, then $ r = 0.05 $. This step ensures the formula is applied correctly.

Step 5: Substitute the values of $ P $, $ r $, and $ n $ into the formula $ A = P(1 + r)^n $ to calculate the accumulated amount. Ensure all values are correctly placed and the exponentiation is performed accurately.