Question

2) Jeff took out a subsidized federal student loan when he was a 2nd year student at CSU-

Pueblo. He borrowed $7500 to pay for his tuition. The federal student loan rate was a fixed APR
of 4.99% with a 1.057% loan distribution fee. He did not pay any interest on the loan while he
was in school and it took him 5 years to graduate from CSU-Pueblo and got a job 3 months after
graduation.
Now it is time for him to pay off her loan. He agreed to pay his loan off in 10 years.
e) How much was his origination fee?
f) How much interest accrued while he was in school?
g) How much will his monthly payment be?
h) How much did he actually pay to borrow the $7500 ?

Answer 1

The origination fee was approximately $79.28. The interest accrued while he was in school was $1867.50. The monthly payment is approximately $80.84. Jeff actually paid approximately $7579.28 to borrow the $7500.

Let's break down the information provided:

Given values:

- Loan amount (\(P\)): $7500

- Annual Percentage Rate (APR): 4.99%

- Loan distribution fee: 1.057%

- Loan term: 10 years

We'll calculate the answers to the questions:

e) How much was his origination fee?

The origination fee is calculated based on the loan amount and the loan distribution fee:

`\[ \text{Origination Fee} = P * \text{Loan Distribution Fee} \]`

Substitute the values:

`\[ \text{Origination Fee} = $7500 * 0.01057 \]`

f) How much interest accrued while he was in school?

Since Jeff did not pay any interest while he was in school, the interest accrued during this time can be calculated using the simple interest formula:

`\[ \text{Interest} = P * r * t \]`

where:

-
`\( P \)` is the principal amount ($7500),

-
`\( r \)`is the annual interest rate (4.99% converted to decimal form),

-
`\( t \)` is the time in years (5 years).

g) How much will his monthly payment be?

The monthly payment can be calculated using the formula for monthly loan payments:

`\[ \text{Monthly Payment} = (P * r * (1 + r)^n)/((1 + r)^n - 1) \]`

where:

-
`\( P \)` is the principal amount ($7500),

-
`\( r \)` is the monthly interest rate (APR divided by 12 and converted to decimal form),

-
`\( n \)` is the total number of payments (loan term in years multiplied by 12).

h) How much did he actually pay to borrow the $7500?

The total amount paid is the sum of the original loan amount and the origination fee.

Let's calculate these values step by step.

e) How much was his origination fee?

`\[ \text{Origination Fee} = $7500 * 0.01057 \]`

`\[ \text{Origination Fee} = $79.275 \]`

So, the origination fee was approximately $79.28.

f) How much interest accrued while he was in school?

`\[ \text{Interest} = $7500 * 0.0499 * 5 \]`

`\[ \text{Interest} = $1867.50 \]`

So, the interest accrued while he was in school was $1867.50.

g) How much will his monthly payment be?

First, convert the APR to a monthly interest rate:

`\[ \text{Monthly Interest Rate} = (0.0499)/(12) \]`

Now, calculate the monthly payment using the loan payment formula:

`\[ \text{Monthly Payment} = \$7500 * 0.004158 * (1 + 0.004158)^(10 * 12)}/{(1 + 0.004158)^(10 * 12) - 1} \]`

Monthly Payments= $80.84

After performing the calculation, the monthly payment is approximately $80.84.

h) How much did he actually pay to borrow the $7500?

The total amount paid is the sum of the original loan amount and the origination fee:

`\[ \text{Total Amount Paid} = $7500 + $79.28 \]`

`\[ \text{Total Amount Paid} = $7579.28 \]`

So, he actually paid approximately $7579.28 to borrow the $7500.