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

What is the formula to calculate the monthly payment (PMT) on a 20-year loan with principal amount $P$, annual interest rate $r$ (compounded monthly), and total number of monthly payments $n$?

PMT = \dfrac{P}{n}

PMT = P \cdot r \cdot n

PMT = \dfrac{P \cdot \left(\dfrac{r}{12}\right)}{1 - (1 + \dfrac{r}{12})^{-n}}

PMT = P \cdot (1 + r)^{n}

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Verified step by step guidance

Step 1: Understand the components of the formula. The monthly payment (PMT) is calculated using the loan principal amount (P), the annual interest rate (r), the number of monthly payments (n), and the monthly interest rate (r/12). The formula accounts for the compounding effect of interest over time.

Step 2: Break down the formula. The correct formula is PMT = \dfrac{P \cdot \left(\dfrac{r}{12}\right)}{1 - (1 + \dfrac{r}{12})^{-n}}. Here, \dfrac{r}{12} represents the monthly interest rate, and (1 + \dfrac{r}{12})^{-n} accounts for the present value of the loan payments over the total number of months.

Step 3: Calculate the monthly interest rate. Divide the annual interest rate (r) by 12 to find the monthly interest rate. This step ensures the interest rate is adjusted for monthly compounding.

Step 4: Compute the denominator of the formula. The denominator is 1 - (1 + \dfrac{r}{12})^{-n}, which represents the discount factor for the loan payments over the total number of months. Use exponentiation to calculate (1 + \dfrac{r}{12})^{-n}.

Step 5: Combine the components. Multiply the principal amount (P) by the monthly interest rate (\dfrac{r}{12}) and divide the result by the denominator calculated in Step 4. This will give the monthly payment (PMT).