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CFI Inc. in York County currently studying the following two potential investments: the first investment pays 2% interest per month, compounded monthly, while the second pays 6% interest per 3 months, compounded quarterly.

a) Determine the effective quarterly interest rate for each of the two investments.

b) Determine the effective annual interest rate for each of the two investments.

c) Which investment should CFI Inc. choose?

d) How much should the interest rate be ( per month, compounded monthly) for the first investment so that neither of the two investments is preferred over the other after one year of investment?

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Darryn D'Souza
Darryn D'SouzaLv10
28 Sep 2019

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Related questions

1. Cash Flow Diagrams and Compounded Interest: John decides to take out a loan for $10,000 for school at an annual interest rate of 10%. He agrees to make four equal payments, but will defer these payments for four years while in school. Starting at the end of the 5th year, he makes four equal annual payments (years 5, 6, 7 and 8). At the end of the 8th year, the loan is paid off.

(a) Create a table that depicts the cash flow diagram for this problem. It should cover years 0 to 8, and should show the balance, interest charges, each payment, how much of that payment went towards interest and how much towards the principal. The balance should be zero at the end of the 8th year. Use trial and error to find the required payment.

(b) Compute the annual payment using one of the built-in Excel functions discussed in class. Show that this gives the same answer as (a).

(c) Compute the present worth and future worth of this investment.

(d) Suppose interest is compounded twice per year instead of annually, but he still makes four annual payments starting at the end of the 5th year. What is the new annual payment?

2. Kate will purchase a house for $500,000 with a 10% down payment and $10,000 in closing costs. The closing costs are included in the loan. A 10-year loan is arranged at 5% interest compounded monthly.

(a) What is the monthly payment?

(b) By choosing to include the closing costs in the loan, how much money was paid in interest on the closing costs over the life of the loan.

(c) What is the effective interest rate for this loan? (Hint: you must take into account the monthly compounding AND the closing costs.)

(d) Suppose closing costs were paid at closing. How does this change the overall cost of the loan? How does this change the effective interest rate?



(NOTE: EVERYTHING SHOULD BE DONE IN EXCEL. OTHERWISE NO POINTS. INCLUDE THE FUNCTION USED AS WELL)

a)Qiqi has overused her credit card. She decides to only pay cash until the balance of $8,574 is paid off. The credit people charge 18% compounded monthly.

How much interest will she owe on the first month's payment?


b)The Bowmanville Town Council has decided that the dam just upstream of the town must be rebuilt and strengthened. The town engineer estimates that it will cost $85,000 by the end of the year. Subsequent annual repair costs will decline by $10,000 per year, making the second year cost $75,000, the third, $65,000 and so on. Council members want to know the equivalent present cost of the repairs for the next 5 years, at 4%. You respond "to the nearest dollar, it will be..."


c)You are setting up your pension fund. You have found an amazing fund that pays 14% compounded continuously. If you deposit $1,200 a month for 7 years, what will be your balance at the end of the seven-year period?


d)A set of cash flows begins at $50,000 and increases at 10% per annum for the next 15 years. If the interest rate is 7%, what is the present value of the set (to the nearest dollar)?



You have $35,259.87 in a brokerage account, and you plan to deposit an additional $2,500 at the end of every future year until your account totals $350,000. You expect to earn 11.7% annually on the account. How many years will it take to reach your goal? Round your answer to the nearest whole number.

2)What is the future value of a 10%, 5-year ordinary annuity that pays $550 each year? Round your answer to the nearest cent.

If this were an annuity due, what would its future value be? Round your answer to the nearest cent.

3)An investment will pay $100 at the end of each of the next 3 years, $300 at the end of Year 4, $500 at the end of Year 5, and $700 at the end of Year 6. If other investments of equal risk earn 9% annually, what is its present value? Round your answer to the nearest cent.

What is its future value? Round your answer to the nearest cent.

4)You want to buy a car, and a local bank will lend you $10,000. The loan would be fully amortized over 6 years (72 months), and the nominal interest rate would be 10%, with interest paid monthly. What is the monthly loan payment? Round your answer to the nearest cent.

What is the loan's EFF%? Round your answer to two decimal places.

5)

Present and Future Values of Single Cash Flows for Different Periods

Find the following values, using the equations, and then work the problems using a financial calculator to check your answers. Disregard rounding differences. (Hint: If you are using a financial calculator, you can enter the known values and then press the appropriate key to find the unknown variable. Then, without clearing the TVM register, you can "override" the variable that changes by simply entering a new value for it and then pressing the key for the unknown variable to obtain the second answer. This procedure can be used in parts b and d, and in many other situations, to see how changes in input variables affect the output variable.)

An initial $800 compounded for 1 year at 5.6%. Round your answers to the nearest cent.

$
An initial $800 compounded for 2 years at 5.6%. Round your answers to the nearest cent.

$
The present value of $800 due in 1 year at a discount rate of 5.6%. Round your answers to the nearest cent.

$
The present value of $800 due in 2 years at a discount rate of 5.6%. Round your answers to the nearest cent.

$

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