Does the “growth” in Part (a) depend on the principal? Support your answer by a brief explanation or computation.

  • Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also; a single file in pdf format is preferred. In your document, be sure to include your name and the assertion of independence of work (see top of the page).
  • If you have any question, please post it in “Ask the Professor” discussion on LEO if the answer to your question would benefit others in class; otherwise, please contact me privately via e-mail.

NOTE:  In financial analyses, the amounts to be reported should be rounded to the nearest cent.

  1. Showing your work,

 

  • (4 points) When subject to an annual simple interest rate of 2%, how long will it take a present value (principal) to “grow” by 50%?

 

  • (2 points) Does the “growth” in Part (a) depend on the principal? Support your answer by a brief explanation or computation.

 

  • ( 4 points) What would be the growth (percent increase) in a principal if it were left in an account subject to an annual interest rate of 2% compounded annually for the length of time found in Part (a)?
  1. (25 points) Consider the following academic problem, involving four independent “savings accounts” A, B, C, and D:

At the end of August,

  1. A deposit of $200.00 is made into a no-interest-bearing account (Account A) and also $200 is deposited into the account at the end of each following month for the rest of the year.
  2. A one-time deposit of $800.00 is made into Account B, subject to an annual simple interest rate of 12%.
  3. A one-time deposit of $800.00 is made into Account C, subject to an annual compound interest rate of 12%, compounded monthly.
  4. A deposit of $200.00 is made into Account D and also $200 is deposited into the account at the end of each following month for the rest of the year, subject to an annual compound interest rate of 12%, compounded monthly.

Showing your work and rounding the answers to two decimal places,

  • Populate the following table, to show the amount at the end of each month for each of the four accounts and the total interest earned at the end of November.

Amount (Future Value) at the end of each month after each end-of-the-month deposit

Account End of August End of September End of October End of November Grand Total Interest Earned at the End of November
A

 

 

         
B

 

 

         
C

 

 

         
D

 

 

         

 

  • Which of the above accounts would be a “Piggy Bank”? Support your answer briefly

 

  • As a “Financial Analyst” in our MATH 106 class, what would you name or label Account D?

 

 

  1. (15 points) When Matthew was born, his grandparents deposited $6000 into a special account for Matthew’s college education. The account earned 7.3% interest compounded daily.
  • How much will be in the account when Matthew is 18?
  • If, upon becoming 18, Matthew arranged for the monthly interest to be sent to him, how much would he receive each 30-day month?

 

 

  1. (15 points) A manufacturing company needs a piece of equipment to be replaced in 5 years at a cost of $900,000.

To have this money available in 5 years, a sinking fund is established requiring making equal monthly payments (at the end of each month; no withdrawals) into an account paying 6.6% compounded monthly.

  • How much should each payment be?
  • How much interest is earned during the last year?

 

 

 

  1. (15 points)Kira buys a refrigerator for her big family for $2,400 and agrees to pay for it in 18 equal monthly payments at an annual interest rate of 18% on the unpaid balance.
  • How much are Kira’s payments?
  • How much interest will she pay?

 

 

 

 

 

 

  1. A family purchased a home 10 years ago for $160,000, paying 20% down and signing a 30-year mortgage at 9% on the unpaid balance.
  • (10 points) How much is the unpaid loan balance after making 120 monthly payments?
  • For Extra Credit (2 points): If equity in a home is defined as

Equity = (current net market value) – (unpaid loan balance), find the equity in the family’s home if its market value is $210,000.

 

 

 

 

 

  1. (10 points) Effective yield, which is also called annual percentage yield [APY], effective interest rate, or true interest rate, is, in effect, the compounded interest on a one-dollar investment after one year.

Following the above interpretation of the effective yield, and invoking the compound interest formula, write the formula for the effective yield for each of the following cases and show your work.  In other words, subtract 1 dollar from the future value of one dollar for each case, having been subjected to a compounding interest for one year.

Calculate the effective yield for the following interest rates:

(a) 4.93% compounded monthly

(b) 4.95% compounded daily

(c) 4.97% compounded quarterly

(d) 4.94% compounded continuously

 

 

 

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