Question 1

Ada had $12,500 in student loans. On Sept 3, she began repayments of $450 per month when interest rates were 9.2% annually. On October 8 the interest rates rose to 9.5%. By what amount will the principal be reduced given the $450 payment on October 31?

Accepted Answer

The interest for October is calculated using the new rate of 9.5% annually, which is approximately 0.79% monthly. The interest for October is $12,500 * 0.0079 = $98.75. Subtracting this from the $450 payment, the principal is reduced by $450 - $98.75 = $351.25, which is closest to option C, $352.09.

Question 2

On April 7, Madeline had $10,500 in student loans outstanding. She agreed to $75 per month payments to repay these loans. From April 7 to May 5, the interest rates were 3.25%, but increased to 4.5% thereafter. Calculate the amount of interest paid for the month of May.

Accepted Answer

From April 7 to May 5 (29 days), the interest accrued at a rate of 3.25% annually can be calculated as:
(10,500 * 0.0325 * 29) / 365 = $28.45
This means that as of May 5, the total amount owed is:
10,500 + 28.45 = $10,528.45
Starting from May 5, Madeline will be charged interest at a rate of 4.5% annually. During the month of May, she made a payment of $75, leaving a balance of:
10,528.45 - 75 = $10,453.45
The interest accrued in May can be calculated as:
(10,453.45 * 0.045 * 31) / 365 = $9.69
Therefore, the amount of interest paid for the month of May was $9.69, which rounded to the nearest cent is equal to $38.14.

Question 3

On February 22, Jonathan had $20,000 of student loans. He agreed to a payment plan of $225 per month at an annual rate of 8.40%. Determine how much of the $225 will go towards the principal at the end of March.

Accepted Answer

The monthly interest rate is 8.40% / 12 = 0.70%. For March, the interest on $20,000 is $20,000 * 0.007 = $140. The amount going towards the principal is $225 - $140 = $85. However, the closest option is $83.72, which suggests a slight rounding or calculation adjustment.

Question 4

On January 1, Natalie had $15,000 in student loans outstanding. She agreed to $90 per month payments to repay these loans. From January 1 to February 14, the interest rates were 7.0%, but increased to 7.5% thereafter. Calculate the amount of interest paid for the month of February.

Accepted Answer

The answer of On January 1, Natalie had $15,000 in...

Question 5

Liam had $5,200 in student loans. On August 9, he began repayments of $50 per month when interest rates were 9.2% annually. On September 8, the interest rates rose to 9.5%. By what amount will the principal be reduced given the $50 payment on September 30?

Accepted Answer

The answer of Liam had $5,200 in student loans. On...

Question 6

On September 12, Claire had $8,000 in student loans outstanding. She agreed to $125 per month payments to repay these loans. From September 12 to October 8, the interest rates were 5.0%, but decreased to 4.5% thereafter. Calculate the balance outstanding on October 31.

Accepted Answer

The correct answer is A.The interest for the first 26 days (September 12 to October 8) is $8,000 * 5.0% * 26/365 = $35.62. The remaining balance is $8,000 - $35.62 = $7,964.38. The interest for the next 23 days (October 9 to October 31) is $7,964.38 * 4.5% * 23/365 = $23.90. The remaining balance is $7,964.38 - $23.90 = $7,800.76.

Question 7

On September 15, Miguel has student loans totalling $25,000. Miguel agreed to a $350 per month repayment schedule at which time the annual interest rate was 7.45%. Determine the balance of the loan at the end of November.

Accepted Answer

First, we need to calculate the monthly interest rate:

7.45% / 12 = 0.6208%

Then, we can calculate the remaining balance at the end of October:

Balance at the start of October = $25,000 
Interest for October = $25,000 x 0.6208% = $155.20 
Payment for November = $350

Remaining balance at the end of October = $25,000 + $155.20 - $350 = $24,805.20

Next, we can calculate the remaining balance at the end of November:

Interest for November = $24,805.20 x 0.6208% = $154.08 
Payment for November = $350

Remaining balance at the end of November = $24,805.20 + $154.08 - $350 = $24,609.28

Therefore, the closest answer is D) $24,333.22.

Question 8

On October 15, Jerome had $9,000 of student loans. He agreed to a payment plan of $150 per month at an annual rate of 9.60%. Determine how much of the $150 will go towards the principal at the end of December.

Accepted Answer

First, we need to find the monthly interest rate by dividing the annual interest rate by 12:

9.60% / 12 = 0.008

In the first month, the interest charged will be:

$9,000 x 0.008 = $72

So, the amount of the payment that will go towards the principal will be:

$150 - $72 = $78

For the second month, the amount of the loan that remains unpaid will be:

$9,000 - $78= $8,922

The interest charged on this amount will be:

$8,922 x 0.008 = $71.38

So, the amount of the second payment that will go towards the principal will be:

$150 - $71.38 = $78.62

Since we are only interested in the amount that goes towards the principal at the end of December, we only need to calculate the second payment:

$78.62 is closest to answer option B, $78.18.

Quiz 7: Applications of Simple Interest