SCENARIO: You are the financial consultant for a young couple who is in need of financial advice.

The couple is looking to earn the most they can on their savings. You have been hired as a financial consultant to help people determine the best options for their savings plans. You need to convince them of the best option for their savings. They currently have $8 000 to invest. The following options are available to them:

keep the money in a saving account bearing 4.75% annual interest, simple interest rate.

1. invest the money in an account bearing 4.1% annual interest, compounded annually

2. invest the money in an account bearing 4.1% annual interest, compounded continuously

3. invest the money in an account bearing 4.1% annual interest, compounded monthly.

a. Determine the equation for the value for the investment as a function of time for each of the four options.

b. Using the Desmos graphing calculator, graph all four functions on the same coordinate plane so each graph is distinguishable.

c. The couple is hoping to buy a home for $120,000 within 10 years. They want to have 10% of that amount saved for a down payment on a house. Write

i. a brief summary to the couple that describes the implications of these options.

ii. The effective yield of a savings plan is the percent increase in the balance after 1 year. Find the effective yields for each of the four options listed above. How could the effective yield be used to decide which option is best?

d. Suppose that the couple purchases a $120,000 home. They reach their goal of 10% down payment and finances the balance through a 30-years mortgage at 3.75% annual rate compounded monthly.

i. How much is their monthly mortgage payment?

ii. How much interest are they going to pay over the life of the loan? iii. Suppose that the couple makes one extra payment of $20 every month; Find the time needed to amortize the loan. About how much will they save in interest?