Three years ago, Isabel got her first job after graduating from college. Once she began earning a steady monthly income, she decided to start saving for a new car. To help her stay on track with her savings, Isabel set up a savings account at her bank and arranged to automatically transfer money into it. On the 15th of every month, the bank transfers $200 from her checking account to her savings account. The interest on her savings account is 1.70% compounded monthly. Part A
Question
Which term best describes the savings account that Isabel has set up, given its purpose?

Select the correct answer.

A. emergency fund
B. mutual fund
C. rainy-day fund
D. sinking fund

Part B
Question
Isabel is shopping for her new car. She identified six models she likes at a local dealership. The table lists the down payment she would need to make on each car to keep the monthly payment within her budget. Assume that she’s using only the money accumulated in her savings account to make the down payment.

Use this information and the appropriate time value of money formula to select all the cars that are within Isabel’s budget.
car price down payment:
8,500
6,200
5,100
7,250
7,750
7,500

Part C
Isabel decided to shop some more. She found a model that she likes even better at a different dealership.

a yellow car with a price tag of $21,950

This car is more affordable than any of Isabel’s previous choices, so she only needs to make a down payment of $5,000 to make the monthly payment fit her monthly budget. The table details the cost of purchasing the car, with and without a down payment of $5,000.

Details With Down Payment of $5,000 No Down Payment
price of car $21,950 $21,950
down payment $5,000 $0
amount financed $16,950 $21,950
interest rate 4.3% compounded monthly 4.8% compounded monthly
loan term 5 years 5 years
The formula to find the payment required for a present value of an annuity will give the payment needed to pay off loans, such as Isabel’s car loan. Here, it’s used to find the monthly loan payment on the car when no down payment is made (PV = present value, P = payment, r = annual interest rate as a decimal, n = compounding periods per year, and t = time in years):

P

=

=

≈ 412.22

Question 1
Question
Use the formula to compute Isabel’s monthly loan payment, assuming that she makes a down payment of $5,000. Recall that the table shows she’ll finance $16,950, and her interest rate is 4.3%.

Type the correct answer in the box. Round the answer to the nearest dollar.

Isabel’s monthly loan payment will be about $
.

Question 2
The down payment makes the monthly loan payment fit into Isabel’s budget. Besides this benefit, do you think saving for a down payment on the car was worth it for Isabel? Use each monthly payment (with and without a down payment) to find the difference of the total amount paid for the car in each scenario to justify your answer.