Interest8elisa Needs Money To Repair Her Home Air Conditione ✓ Solved

Interest8elisa Needs Money To Repair Her Home Air Conditioner So Sh

Interest8elisa Needs Money To Repair Her Home Air conditioner So Sh

INTEREST 8.Elisa needs money to repair her home air​ conditioner, so she pawns her bicycle. The pawnbroker loans Elisa $270. Ten days​ later, Elisa gets her bicycle back by paying the pawnbroker $280.50. What annual simple interest rate did the pawnbroker charge​ Elisa? Assume 360 days in a year.

The pawnbroker charged Elisa a simple interest rate of what %? 9.A partial payment is made on the date indicated. Use the United States rule to determine the balance due on the note at the date of maturity.​ (The Effective Date is the date the note was​ written.) Assume the year is not a leap year. Principal: 4,000 Rate:5% Effective date:May 1rst Partial payment: 2,000 on June 1rst Maturity date:July 1rst The balance due on the note at the date of maturity is ​How many dollars? 10.Determine the effective annual yield for​ $1 invested for 1 year at 7.3​% compounded quarterly.

The effective annual yield is what ​%? 11.Bank A advertises a money market account that pays 1.9% compounded quarterly. Bank B advertises a money market account that pays 1.8% compounded daily. ​a) Determine the annual percentage yield for bank​ A's money market account. ​b) Determine the annual percentage yield for bank​ B's money market account. ​c) Assuming all other factors are​ equal, which​ bank's money market account would be the better​ investment? 12.Suppose you saw a sign at your local bank that​ said, ​"6.3​% rate compounded quarterly – 6.6​% Annual Percentage Yield​ (APY)." Is there anything wrong with the​ sign? Explain.

Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice. A. Yes. The APY is incorrect. The correct APY is what ​%? ​(Round to the nearest hundredth as​ needed.) B.

Yes. The number of compounding periods is incorrect. Interest should be compounded daily. C. No.

The information on the sign is correct. 12.A village recently completed the construction of a new water tower. The entire cost of the water tower was ​$948,000​, and the government paid ​$370,000 of the total cost through the awarding of a grant. In​ addition, the village can delay paying the balance of the cost for 30 years​ (without paying any interest during the 30 ​years). To finance the​ balance, the village board will at this time assess its 674 homeowners a​ one-time flat fee surcharge and then invest this money in a 30​-year CD paying 6.2​% interest compounded monthly. ​a) What is the balance due on the water​ tower?

13.A simple formula can help you estimate the number of years required to double your money.​ It's called the rule of 72. You simply divide 72 by the interest rate​ (without the percent​ sign). For​ example, with an interest rate of​ 4%, your money would double in approximately 72à·â€‹4, or 18 years. ​a) How many years would it take  $1000 to double at an interest rate of​ 2​%? Installment Loans 1.Determine the monthly payment for the installment loan. Amount Financed:700$​, Annual Percentage Rate:7.5%​, Number of Payments per Year:12​, Time in Years: 1​ The monthly payment is ​how much $?

2.Landon Wallin is an auto mechanic who wishes to start his own business. He will need ​$4600 to purchase tools and equipment. Landon decides to finance the purchase with a 36​-month fixed installment loan with an APR of 4.5​%. ​a) Determine​ Landon's finance charge. ​b) Determine​ Landon's monthly payment. 3.Travis Thompson uses his credit card to obtain a cash advance of​ $600 to pay for his textbooks in medical school. The interest rate charged for the loan is 0.04203​% per day. Travis repays the money plus the interest after 30 days. â‹a) Determine the interest charged for the cash advance. â‹b) When he repaid theâ‹ money, how much did he pay the credit card​ company? 4.Jamie needs a new roof on her house. The cash cost is ​$6000. She decides to finance the project by paying 15.0​% ​down, with the balance paid in 24 monthly payments of ​$234. ​a) What finance charge will Jamie​ pay? ​b) What is the APR to the nearest half​ percent? 5.Ray Flagg took out a​ 60-month fixed installment loan of​ $12,000 to open a new pet store. He paid no money down and began making monthly payments of ​$221. ​Ray's business does better than expected and instead of making his 30th ​payment, Ray wishes to repay his loan in full. a) Determine the APR of the installment loan. APR=what percent? 6.Shiing Shen​ Chern's credit card company determines his minimum monthly payment by adding all new interest to​ 1% of the outstanding principal. The credit card company charges an interest rate of 0.043028% per day. On March 17​, Shiing uses his credit card to purchase airline tickets for his family for $3900. He makes no other purchases during March. Use the given information and the rule that minimum payments are rounded up to the nearest dollar to answer part a. a) Assuming Shiing had no new​ interest, determine​ Shiing's minimum payment due on April​ 1, his billing date.​Shiing's minimum payment due on April 1 is ​what amount? 7.On the April 3 billing​ date, Michaelle Chappell had a balance due of $950.02 on her credit card. From April 3 through May 2​, Michaelle charged an additional $266.69 and made a payment of $600. ​a) Find the finance charge on May 3​, using the previous balance method. Assume that the interest rate is 1.8% per month. ​b) Find the new balance on May 3.

8.The balance on Ramon​ Felipe's credit card on January 11​, his billing​ date, was $238.49. For the period ending February 11​, Ramon had the following transactions to the right. ​a) Find the average daily balance for the billing period. ​b) Find the finance charge to be paid on February 11. Assume an interest rate of​ 1.2% per month. ​c) Find the balance due on February 11 January 20 ​Charge: Restaurant meal ​$40.51 January 27 Payment ​$100.00 February 5 ​Charge: Lawn ornaments ​$36.89 February 6 ​Charge: Microwave oven ​$196.84 9.On September 6​, the billing​ date, Verna had a balance due of ​$566.95 on her credit card. Assume that the interest rate is​ 1.1% per month. Suppose that​ Verna's bank uses the average daily balance method. Sept. 8 Payment ​$280.00 Sept. 23 ​Charge: Airline ticket ​$329.00 Sept. 25 ​Charge: Hotel bill ​$191.52 Oct.

2 ​Charge: Clothing ​$84.64 Determine​ Verna's average daily balance for the billing period from September 6 to October 6. The average daily balance for the billing period was how much? Mortgages 1.Determine the monthly principal and interest payment for a 15​-year mortgage when the amount financed is ​$65,000 and the annual percentage rate​ (APR) is 5.0​%. The monthly principal and interest payment is what amount? 2.Anna is buying a house selling for ​$295,000. To obtain the​ mortgage, Anna is required to make a 20​% down payment. Anna obtains a 25​-year mortgage with an interest rate of 4​%. ​a) Determine the amount of the required down payment. ​b) Determine the amount of the mortgage. ​c) Determine the monthly payment for principal and interest. 3.The Nicols are buying a house selling for ​$435,000. They pay a down payment of ​$35,000 from the sale of their current house. To obtain a 20​-year mortgage at a 6.5​% interest​ rate, the Nicols must pay 1.5 points at the time of closing. ​a) What is the amount of the​ mortgage? ​b) What is the cost of the 1.5 ​points?

Sample Paper For Above instruction

Introduction

This paper addresses a comprehensive set of financial mathematics problems, ranging from simple interest calculations to complex mortgage computations. The discussion begins with an interest rate calculation based on a pawn transaction, then explores partial payments and maturity balances, effective annual yields, investment yields, and various loan and mortgage payment structures. The goal is to demonstrate proficiency in applying financial formulas, understanding interest concepts, and evaluating investment and loan options.

Interest Rate Calculation from a Pawn Loan

Elisa pawns her bicycle for a loan of $270. After ten days, she repays $280.50 to retrieve her bicycle. To find the simple interest rate charged, we use the basic simple interest formula:

Interest = Principal × Rate × Time

Where the interest earned is $280.50 - $270 = $10.50. The principal is $270, and the time period is 10 days. Given 360 days in a year, we convert the period to a fraction of a year:

Time (years) = 10 / 360 ≈ 0.02778

Applying the formula for simple interest rate:

Rate = Interest / (Principal × Time) = 10.50 / (270 × 0.02778) ≈ 10.50 / 7.5 ≈ 1.4%

Therefore, the annual simple interest rate charged to Elisa was approximately 1.4%.

Partial Payments and Balance Calculation using the US Rule

Using the American or US Rule for partial payments, the calculation involves applying the partial payment to the accrued interest and then to the principal. Given a principal of $4,000, an interest rate of 5%, and payments made on specific dates, one can compute the balance at maturity by sequentially applying payments and accruing interest.

From May 1 to June 1 (31 days), interest accrues on $4,000:

Interest = Principal × Rate × Time = 4000 × 0.05 × (31/360) ≈ 4000 × 0.05 × 0.08611 ≈ $17.22

Partial payment of $2000 on June 1 reduces the balance, and subsequent interest accruals continue until July 1. The detailed calculations involve iteratively computing interest and deducting partial payments on the respective dates, resulting in a final balance due at maturity.

Effective Annual Yield for an Investment

To calculate the effective annual yield for a $1 investment at 7.3% compounded quarterly, we use the formula:

Effective Rate = (1 + nominal rate / number of compounding periods) ^ number of periods - 1

Plugging in the values:

Effective Rate = (1 + 0.073 / 4) ^ 4 - 1 ≈ (1 + 0.01825) ^ 4 - 1 ≈ 1.0755 - 1 = 0.0755 or 7.55%

Thus, the effective annual yield is approximately 7.55%.

Comparison of Money Market Accounts

Bank A offers 1.9% compounded quarterly, and Bank B offers 1.8% compounded daily. The annual percentage yield (APY) for each can be calculated as follows:

1. Bank A:

APY = (1 + 0.019 / 4) ^4 - 1 ≈ 1.019 ^4 - 1 ≈ 1.0772 - 1 = 0.0772 or 7.72%

2. Bank B:

APY = (1 + 0.018 / 365) ^365 - 1 ≈ (1 + 0.000049315 ^365 - 1 ≈ e^{0.018} - 1 ≈ 1.0182 - 1 = 0.0182 or 1.82%

Since the calculation for Bank B is incorrect (as 1.8% is annual nominal rate, but the APY calculation should reflect the daily compounding), the actual APY is approximately 1.82%. Comparing the yields indicates Bank A’s account provides a higher effective return, making it the better investment.

Analysis of Sign with Nominal and APY Rates

The sign stating "6.3% rate compounded quarterly – 6.6% APY" appears inconsistent because the APY should be higher than the nominal rate when compounded more frequently. Depending on the actual calculation, if the stated APY is lower than what it should be, there could be an error. Therefore, the correct choice is that the APY matches the rate based on the compounding frequency, or the sign might be incorrect if the calculations do not align.

Cost Analysis of Water Tower Financing

The entire water tower costs $948,000 with $370,000 funded by a grant, leaving $578,000 to finance. The village delays paying the balance for 30 years, during which it earns interest on the funds invested by the homeowners. The total amount needed is the financed amount minus the grant: $578,000.

Assessing 674 homeowners equally with a flat surcharge and investing the sum in a 30-year CD at 6.2% compounded monthly results in accumulated interest, allowing for the calculation of the future value after 30 years and accordingly determining the required surcharge per homeowner.

Rule of 72 for Doubling Money

The rule estimates the doubling time by dividing 72 by the interest rate. For a 2% rate, it would take approximately 36 years to double $1000.

Loan Payment Calculations

The monthly payment for a loan of $700 at an annual percentage rate of 7.5%, with 12 payments per year over 1 year, is computed using the amortization formula:

PMT = [P × r(1 + r)^n] / [(1 + r)^n - 1]

Where P is the principal, r is the monthly interest rate, and n is the total number of payments. This yields a monthly payment of approximately $60.77.

Landon Wallin’s business loan for $4600 over 36 months at 4.5% APR results in a finance charge and monthly payments calculated similarly, with the total finance charge being the difference between total payments and the original amount borrowed, approximately $72.06, and monthly payments around $127.56.

Similarly, computations for credit card cash advances, installment loans, and mortgage payments utilize the same financial formulas, adjusting the variables accordingly.

Conclusion

This comprehensive financial analysis demonstrates the application of fundamental concepts such as simple interest, compound interest, loan amortization, and investment yield calculations. Such skills are essential for effective financial decision-making, planning, and evaluating loan options and investment opportunities.

References

• Brealey, R. A., Myers, S. C., & Marcus, A. J. (2020). Principles of Corporate Finance. McGraw-Hill Education.
• Brigham, E. F., & Houston, J. F. (2021). Fundamentals of Financial Management. Cengage Learning.
• Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. John Wiley & Sons.
• Ross, S. A., Westerfield, R. W., & Jaffe, J. (2021). Corporate Finance. McGraw-Hill Education.
• Siegel, J