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

Jorge takes out a loan of $10,000 at an annual interest rate of 6%, compounded annually. If he makes equal annual payments of $2,000 at the end of each year, approximately how many years will it take Jorge to pay off the loan?

7 years

5 years

6 years

8 years

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Verified step by step guidance

Step 1: Understand the problem. Jorge has taken a loan of $10,000 with an annual interest rate of 6%, compounded annually. He makes equal annual payments of $2,000 at the end of each year. The goal is to determine how many years it will take to pay off the loan.

Step 2: Use the formula for the present value of an ordinary annuity to calculate the number of years required to pay off the loan. The formula is: $ PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} $, where $ PV $ is the loan amount ($10,000), $ PMT $ is the annual payment ($2,000), $ r $ is the annual interest rate (6% or 0.06), and $ n $ is the number of years.

Step 3: Rearrange the formula to solve for $ n $, the number of years. This involves isolating $ n $ and using logarithms to solve for the exponent. The rearranged formula is: $ n = \frac{\log(1 - \frac{PV \times r}{PMT})}{\log(1 + r)} $.

Step 4: Substitute the known values into the formula. $ PV = 10,000 $, $ PMT = 2,000 $, and $ r = 0.06 $. Perform the calculations step by step, starting with $ \frac{PV \times r}{PMT} $, then $ 1 - \frac{PV \times r}{PMT} $, and finally apply the logarithms.

Step 5: Interpret the result. The calculated $ n $ will represent the approximate number of years it will take Jorge to pay off the loan. Compare the result to the provided options (7 years, 5 years, 6 years, 8 years) to identify the correct answer.