85.6k views
2 votes
Consider a student loan of 7500 at a fixed APR of 9% for four years

Calculate the monthly payment
Determine the total amount paid over the term of the loan of the total amount paid what percentage is paid toward the principal, and what percentage is paid for the interest

User Allen Chou
by
8.3k points

1 Answer

4 votes

Answer:

Explanation:

To calculate the monthly payment for a student loan, you can use the loan payment formula. The formula for calculating the monthly payment (PMT) is:

PMT = (P * r * (1 + r)^n) / ((1 + r)^n - 1)

Where:

P = Principal amount (loan amount) = $7500

r = Monthly interest rate = (Annual interest rate / 12) = 9% / 12 = 0.75%

n = Number of payments = 4 years * 12 months = 48 months

Let's calculate the monthly payment:

PMT = (7500 * 0.0075 * (1 + 0.0075)^48) / ((1 + 0.0075)^48 - 1)

PMT ≈ $183.64 (rounded to two decimal places)

Therefore, the monthly payment for the student loan is approximately $183.64.

To determine the total amount paid over the term of the loan, you can simply multiply the monthly payment by the number of payments:

Total amount paid = Monthly payment * Number of payments

Total amount paid = $183.64 * 48

Total amount paid = $8,815.52

So, the total amount paid over the term of the loan is $8,815.52.

To calculate the percentage paid toward the principal and the interest, we need to know the breakdown of each payment. Since the interest rate is fixed, we can calculate the interest portion for each payment using the following formula:

Interest portion = Principal balance * Monthly interest rate

The principal portion can be calculated by subtracting the interest portion from the monthly payment.

Let's calculate the breakdown for each payment:

First, calculate the total interest paid over the loan term by summing up the interest portions for each payment:

Total interest paid = (Interest portion of payment 1 + Interest portion of payment 2 + ... + Interest portion of payment 48)

To calculate the principal portion and interest portion for each payment, we'll use a loop. Here's the breakdown:

Principal balance = $7500

Total interest paid = 0

for each payment from 1 to 48:

Interest portion = Principal balance * Monthly interest rate

Principal portion = Monthly payment - Interest portion

Total interest paid += Interest portion

Principal balance -= Principal portion

After executing this loop, we'll have the principal and interest breakdown for each payment, and the total interest paid over the loan term. Let's calculate it:

Principal balance = $7500

Total interest paid = 0

Principal breakdown = []

Interest breakdown = []

for payment in range(1, 49):

Interest portion = Principal balance * 0.0075

Principal portion = 183.64 - Interest portion

Total interest paid += Interest portion

Principal balance -= Principal portion

Principal breakdown.append(Principal portion)

Interest breakdown.append(Interest portion)

Percentage paid toward principal = (Total principal paid / Total amount paid) * 100

Percentage paid toward interest = (Total interest paid / Total amount paid) * 100

Calculating this, we find:

Total interest paid ≈ $1,315.52

Percentage paid toward principal ≈ (7500 / 8815.52) * 100 ≈ 85.06%

Percentage paid toward interest ≈ (1315.52 / 8815.52) * 100 ≈ 14.94%

Therefore, over the term of the loan, approximately 85.06% of the total amount paid goes toward the principal, while approximately 14.94% goes toward interest.

User Bk Lim
by
7.9k points

No related questions found