3-3 Student Loans - C

Multiple Choice

Bellwork:

Evaluate

• 4.54 and -0.18

• 4.5 and -0.2

• 4 and -0.1

• 4.6 and 0

Financial Algebra Second Edition

Slide 2

Learning Goals 3-3 Student Loans

The students will be able to:

• Explain the options available for student loans.
• Calculate the interest due in various student loan situations.
• Apply the simplified daily interest formula.

Financial Algebra Second Edition

Slide 3

Example 1
As an incoming college freshman, Ariana received a 10-year, $9,100 Federal Direct Unsubsidized Loan with an interest rate of 4.29%. She knows that she can begin making loan payments 6 months after
graduation, but interest will accrue from the moment the funds are credited to her account. How much interest will accrue while she is still in school and over the 6-month grace period for this freshman-year loan? (I = Prt)

Financial Algebra Second Edition

Slide 3

​Solution

With an unsubsidized loan, students are responsible for interest accrued while they are in school and during the grace period. While they don’t have to start loan payments until 6 months after they leave school, the interest starts to accrue as soon as funds are credited.

The student loan interest during the nonpayment period is calculated using the simple interest formula:

P = 9,100; r = 0.0429; t = 4.5   (4 years plus 6 months grace period)

​Her new principal at the end of 4.5 years is the sum of the loan amount, $9,100, and the interest, $1,756.76.

Multiple Select

Write the formula for the amount of interest that would accrue over 4 years in college plus a 6-month grace period on a Y-year loan in the amount of A dollars at an interest rate of R.

• $$\frac{4.5AR}{100}$$

• $$4.5A\ \left(\frac{R}{100}\right)$$

• $$4.5AR$$

• $$4.5ART$$

Financial Algebra Second Edition

Slide 6

Example 2

Ariana can elect to defer all payments during the 4.5-year period. Her loan balance would then be the sum of the amount borrowed and the interest accrued over the 4.5-year nonpayment period. Determine the interest she would pay on this loan.
(10-year, $9,100, 4.29%)

Financial Algebra Second Edition

Solution
The new principal P is the sum of the loan amount and the interest accrued during the nonpayment period found in Example 1.

P = 9,100 + 1,756.76
P = 10,856.76

Use the monthly payment formula:

Her monthly payments would be approximately $111.42.
Her total payments ($111.42 × 120) would be $13,370.40. Her interest for the loan is $13,370.40 – 9,100, or $4,270.40. This brings the total payment for the loan to $13,370.40.

Multiple Choice

Luke took out a 10-year Federal Direct Unsubsidized loan for $15,000 with a 4.29% APR. If he makes no payments during the first 4.5 years, what will the new loan amount be?

• $12,097.50

• $17,895.75

• $32,902.50

• $43,537.50

Financial Algebra Second Edition

Practice:

Textbook lesson 3.3
Exercises # 2 & 4