1. Showing your work,

(a) 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%.

(b) Does the doubling time found for Part (a) depend on the amount invested (PV)? Briefly explain your answer in words and/or mathematically.

(c) Determine the growth factor for a present value (the ratio of FV to PV) if it were left in an account for the time duration found in Part (a) but subject to an annual interest rate of 8% compounded annually. (HINT: You may solve for the ratio before substituting values.)

(d) Compare Parts (a) and (c) and their solutions; briefly explain your observation. (e) (2 points) 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. Consider the following academic problem, involving four independent savings accounts A, B, C, and D:

At the end of March,

A. A deposit of $100.00 is made into a no-interest-bearing account (Account A) and also $100 is deposited into the account at the end of each month for the rest of the year.

B. A one-time deposit of $400.00 is made into Account B, subject to an annual simple interest rate of 12%.

C. A one-time deposit of $400.00 is made into Account C, subject to an annual compound interest rate of 12%, compounded monthly.

D. A deposit of $100.00 is made into Account D and also $100 is deposited into the account at the end of each 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. Amount at the end of each month after each end-of-the-month deposit Account End of March End of April End of May End of June Total Interest Earned A B C D 3.

(9 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. 4. (9 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.

5. It can be said that the 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.

(a) (3 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) (3 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).

6. (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.

7. 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) (5 points) Calculate the monthly payment. Show how to carry out the calculation.

(b) (8 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) (4 points) Calculate the total interest paid if the loan is held for the entire term. Show some work.

(d) (4 points) Calculate the unpaid balance after 3 years. Show work.

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

8. (5 points) 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.