Project #72544 - Math 106

1.    Showing your work,

(a)    (2.5 points) Write the simple interest formula, using FV (future value) for the total amount, and PV (present value) for the principal.

 

(b)   (2.5 points) Write the compound interest formula, using FV for the total amount, and PV for the principal.

 

(c)    (5 points) Determine how long it would take to double a present value if it were left in an account subject to an annual simple interest rate of 8%.

 

(d)   (5 points) Does the doubling time in Part (c) depend on the amount invested (PV)? Briefly explain your answer in words and/or mathematically.

 

(e)    (5 points) Determine the growth factor (the ratio of FV to PV) for a present value if it were left in an account for the time duration found in Part (c) but subject to an interest rate of 8% compounded annually.

 

(f)    (2 point) Comparing the answers to Parts (c) and (e), briefly explain the reason for the results of your comparison.

 

(g)   (5 points) FOR EXTRA CREDIT - Determine how long it would take to double a present value if it were left in an account subject to an annual interest rate of 8% compounded annually.

 

2. (10 points) A credit card balance of $13,095 was one month overdue and the owner of the account was charged $158.23 as the interest for one month. What annual interest rate did the credit card company apply to the balance? Show work.

 

3. (10 points) pts) John arranges for $28,575 of home improvement work to be done on his house, financed with a monthly payment for three and a half years. He calculated that he would pay a total interest of $1837. Determine the monthly payment.  Show work/explanation.

 

4. It can be said that the effective yield, which is also called (annual percentage yield [APY], or effective interest rate, or true interest rate, is, in effect, the compounded interest on a one-dollar investment after one year.

(a) (5 points) Following the above interpretation of the effective yield, and invoking the compound interest formula, write the formula for the effective yield.  In other words, subtract 1 dollar from the future value of one dollar, having been subject to a compounding interest for one year.

(b) (8 points) Calculate the effective yield for the following interest rates:

4.93% compounded monthly

4.95% compounded daily

4.97% compounded quarterly

4.94% compounded continuously

(c) (5 points) What is the benefit of calculating effective yield when comparing different offers for the interest rate? Support your answer by referring to your answers to Part (b).

 

 

5. (10 pts) A couple has set up a sinking fund in order to have $40,000 in 5 years for the down payment on a house. How much should be paid quarterly into an account paying 5.8% annual interest compounded quarterly? Show work.

 

 

 

6. To purchase a house, a homebuyer takes out a mortgage, borrowing $285,000 at the annual interest rate 4.8%, compounded monthly for 30 years.  (The problem has five parts.)

(a) (6 points) Calculate the monthly payment. Show how to carry out the calculation.

 

 

 

 

(b) (12 points) Complete the following table. (Round amounts to the nearest cent.)

 

Payment number

Interest Paid

Principal Paid

Unpaid balance

1

 

 

 

 

2

 

 

 

 

 

Show the calculations necessary to arrive at the entries in the table.

 

 

 

 

 

(c) (5 points) Calculate the total interest paid if the loan is held for the entire term. Show some work.

 

 

(d) (5 points) Calculate the unpaid balance after 3 years. Show work.

 

 (e)  (2 points) What percentage of the amount borrowed is still unpaid?

 

 

 

 

 

7. (5 points) FOR EXTRA CREDIT - A family purchased a home 20 years ago for $200,000 by paying 20% down and signing a 30-year mortgage at 13.2% compounded monthly. Showing your work, calculate the total interest paid in the first 20 years.

 

8.   You invested $10,000 into two accounts: one that has simple 3% interest, the other with 2.5% interest. If your total interest payment after one year was $283.50, how much was in each account after the year passed?

 

COMPOUND INTEREST

9.       How much should be invested at 10.3% for it to amount to $10,000 in 6 years?

 

 

Solve

 

10.   The perimeter of a square is 44 inches. Find the length of a side.

 

 

 

 

 

Subject Mathematics
Due By (Pacific Time) 05/31/2015 05:00 pm
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