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

When determining the accumulation value of a deferred annuity, which formula is most appropriate to use?

Present Value of an Ordinary Annuity: \( PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} \)

Future Value of a Single Sum: \( FV = PV \times (1 + r)^n \)

Future Value of an Ordinary Annuity: \( FV = PMT \times \frac{(1 + r)^n - 1}{r} \)

Present Value of a Single Sum: \( PV = \frac{FV}{(1 + r)^n} \)

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Verified step by step guidance

Step 1: Understand the concept of a deferred annuity. A deferred annuity involves periodic payments (PMT) that begin after a certain deferral period, and the accumulation value refers to the total value of these payments at a future date, including interest earned.

Step 2: Identify the correct formula for the accumulation value of a deferred annuity. The formula for the Future Value of an Ordinary Annuity is: \( FV = PMT \times \frac{(1 + r)^n - 1}{r} \), where \( r \) is the interest rate per period, \( n \) is the number of periods, and \( PMT \) is the periodic payment.

Step 3: Break down the formula. The term \( (1 + r)^n \) represents the compounding factor over \( n \) periods, \( (1 + r)^n - 1 \) calculates the total growth minus the initial principal, and dividing by \( r \) adjusts for the periodic payment structure.

Step 4: Apply the formula to the problem. Substitute the given values for \( PMT \), \( r \), and \( n \) into the formula \( FV = PMT \times \frac{(1 + r)^n - 1}{r} \). Ensure that the interest rate \( r \) is expressed as a decimal (e.g., 5% = 0.05).

Step 5: Perform the calculations step by step. First, calculate \( (1 + r)^n \), then subtract 1, divide the result by \( r \), and finally multiply by \( PMT \) to find the accumulation value. This will give the future value of the deferred annuity.