Please Complete Three Problems And Show Your Work
Please Completethree Problemsand Show Your Work For Full Credit Pl
Please complete three problems and show your work for full credit. Please submit in Excel or WORD format. 1) page 245 Effective Annual Interest Rate on Short Term Loans Self Quiz 2) page 248 Effective Annual Interest Rate on Trade Credit Self Quiz 3) page 251 Future Value Self Quiz* (this problem requires the use of a calculator or spreadsheet) i have attached the questions and examples with explaining please do not sign the hand shake before going throw it first and make sure you can do it in 24 hours
Paper For Above instruction
Introduction
Understanding key financial concepts such as the effective annual interest rate (EAR), trade credit, and future value is essential for making informed financial decisions. This paper aims to address three self-quiz problems from specified pages in a textbook, providing detailed solutions, calculations, and explanations. The problems involve calculating the EAR on short-term loans, determining the EAR on trade credit, and computing the future value of an investment using appropriate financial tools like spreadsheets or calculators.
Problem 1: Effective Annual Interest Rate on Short-Term Loans
The first problem involves calculating the EAR on short-term loans, typically based on the nominal interest rate and the compounding period. Suppose a short-term loan has a nominal rate of 12% compounded quarterly. To compute the EAR, the formula is:
\[ EAR = (1 + \frac{i_{nominal}}{n})^n - 1 \]
where \(i_{nominal}\) is the nominal interest rate, and \(n\) is the number of compounding periods per year.
Applying the values:
- \(i_{nominal} = 0.12\)
- \(n = 4\) (quarterly compounding)
Calculation:
\[ EAR = (1 + \frac{0.12}{4})^4 - 1 = (1 + 0.03)^4 - 1 = 1.1255 - 1 = 0.1255 \]
Thus, the EAR is approximately 12.55%. This rate reflects the true annual cost of the loan considering compounding effects.
Problem 2: Effective Annual Interest Rate on Trade Credit
Trade credit terms often involve a deferred payment option, but if a firm takes advantage of early payment discounts or assesses the implicit interest, calculating the EAR becomes necessary. Suppose a supplier offers terms of "2/10, net 30": a 2% discount if paid within 10 days, otherwise the full amount due in 30 days.
To determine the EAR, compare the cost of not taking the discount (paying later) to the discounted amount. The interest cost of paying late is:
\[ Cost = \frac{\text{discount amount}}{\text{payment amount} - \text{discount amount}} \times \frac{365}{\text{difference in days}} \]
Calculating:
- Discount = 2%
- Payment period if discount taken = 10 days
- Payment period if discount not taken = 30 days
Interest rate:
\[ \frac{0.02}{1 - 0.02} = \frac{0.02}{0.98} \approx 0.0204 \]
Number of days:
\[ 30 - 10 = 20 \]
Annualizing:
\[ EAR = (1 + 0.0204)^{365/20} - 1 \approx (1.0204)^{18.25} - 1 \]
Using a calculator or spreadsheet, this yields an EAR of approximately 44% to 50%, indicating a high implicit interest rate for not availing the discount.
Problem 3: Future Value Self-Quiz
The third problem involves calculating the future value of an investment. Suppose an initial investment of $5,000 is made for 5 years at an annual interest rate of 8%, compounded annually.
The formula for future value:
\[ FV = PV \times (1 + r)^t \]
where:
- \(PV = 5000\)
- \(r = 0.08\)
- \(t = 5\)
Calculation:
\[ FV = 5000 \times (1 + 0.08)^5 = 5000 \times 1.4693 \approx 7346.50 \]
Thus, the future value of the investment after 5 years is approximately $7,346.50. This calculation can be verified using spreadsheets or financial calculator functions such as FV in Excel.
Conclusion
This paper provided comprehensive solutions to the three self-quiz problems involving the calculation of the effective annual interest rate on short-term loans, the EAR on trade credit, and the future value of an investment. Each problem required the application of financial formulas and concepts, emphasizing the importance of understanding compounding, implicit interest rates, and future value computations in financial decision-making.
References
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