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

Carlin has a mortgage with a remaining balance of $120,000 at an annual interest rate of 4ext{%} compounded monthly. Her current monthly payment is $800, but she considers increasing it to $1,200 per month. If she starts making the higher payment in January 2024, in which month and year will she pay off her house?

August 2029

December 2035

June 2032

March 2030

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Verified step by step guidance

Step 1: Understand the problem. Carlin has a mortgage with a remaining balance of $120,000, an annual interest rate of 4% compounded monthly, and she is considering increasing her monthly payment from $800 to $1,200 starting January 2024. The goal is to determine when she will pay off her mortgage with the higher payment.

Step 2: Calculate the monthly interest rate. Since the annual interest rate is 4%, divide it by 12 to find the monthly interest rate: $ \text{Monthly Interest Rate} = \frac{4}{100 \times 12} $.

Step 3: Use the formula for the remaining balance of a loan to calculate the time required to pay off the mortgage. The formula is $ B = P \times \frac{1 - (1 + r)^{-n}}{r} $, where $ B $ is the loan balance, $ P $ is the monthly payment, $ r $ is the monthly interest rate, and $ n $ is the number of months. Rearrange the formula to solve for $ n $, the number of months required to pay off the loan.

Step 4: Substitute the values into the formula. Use $ B = 120,000 $, $ P = 1,200 $, and $ r $ (calculated in Step 2). Solve for $ n $, which represents the number of months required to pay off the loan with the higher payment.

Step 5: Convert the number of months $ n $ into a specific month and year. Add $ n $ months to January 2024 to determine the payoff date. Compare the calculated payoff date to the options provided (August 2029, December 2035, June 2032, March 2030) to identify the correct answer.