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

Inga has an outstanding loan with a remaining balance of $12,000. She makes fixed annual payments of $3,000 at an annual interest rate of 5\%. Using the time value of money equations, how many more years will it take Inga to pay off the loan?

6 years

3 years

4 years

2 years

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Verified step by step guidance

Identify the key variables in the problem: the loan balance (Present Value, PV) is $12,000, the fixed annual payment (PMT) is $3,000, the annual interest rate (r) is 5% or 0.05, and the unknown is the number of years (n) required to pay off the loan.

Use the Present Value of an Ordinary Annuity formula to solve for the number of years (n): $ PV = PMT \times \frac{1 - (1 + r)^{-n}}{r} $. Rearrange this formula to isolate $ n $.

Rearranging the formula: $ \frac{PV \times r}{PMT} = 1 - (1 + r)^{-n} $. Then, isolate $ (1 + r)^{-n} $: $ (1 + r)^{-n} = 1 - \frac{PV \times r}{PMT} $.

Take the natural logarithm (ln) of both sides to solve for $ n $: $ -n \times \ln(1 + r) = \ln(1 - \frac{PV \times r}{PMT}) $. Finally, solve for $ n $: $ n = -\frac{\ln(1 - \frac{PV \times r}{PMT})}{\ln(1 + r)} $.

Substitute the known values into the formula: $ PV = 12000 $, $ PMT = 3000 $, $ r = 0.05 $. Perform the calculations step by step to determine $ n $, the number of years required to pay off the loan.