Consider a student loan of $17,500 at a fixed APR of 12% for 20 years.
a. Calculate the monthly payment.
b. Determine the total amount paid over the term of the loan.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest.
a. The monthly payment is $179.03.
b. The total amount paid over the term of the loan is $43,814.80.
c. Of the total amount paid, $26,314.80 is paid for interest (60%) and $17,500 is paid toward the principal (40%).
To calculate the monthly payment, we can use the formula for a fixed-rate loan:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal amount (loan amount)
r = Monthly interest rate (APR / 12)
n = Number of payments (loan term in months)
a. Calculate the monthly payment:
P = $17,500
APR = 12%
n = 20 years = 20 * 12 = 240 months
r = 12% / 12 = 0.01 (monthly interest rate)
M = $17,500 * (0.01 * (1 + 0.01)^240) / ((1 + 0.01)^240 - 1)
M ≈ $193.33
Therefore, the monthly payment is approximately $193.33.
b. Determine the total amount paid over the term of the loan:
Total amount paid = Monthly payment * Number of payments = $193.33 * 240
Total amount paid ≈ $46,399.20
Therefore, the total amount paid over the term of the loan is approximately $46,399.20.
c. To find the percentage of the total amount paid toward the principal and interest, we need to calculate the total interest paid.
Total interest paid = Total amount paid - Principal amount
Total interest paid = $46,399.20 - $17,500
Total interest paid ≈ $28,899.20
Percentage paid toward the principal = (Principal amount / Total amount paid) * 100
Percentage paid toward the principal = ($17,500 / $46,399.20) * 100
Percentage paid toward the principal ≈ 37.76%
Percentage paid for interest = (Total interest paid / Total amount paid) * 100
Percentage paid for interest = ($28,899.20 / $46,399.20) * 100
Percentage paid for interest ≈ 62.24%
Therefore, approximately 37.76% of the total amount paid is paid toward the principal, and approximately 62.24% is paid for interest.
To calculate the monthly payment, total amount paid, and the percentage paid toward principal and interest, we can use the formula for calculating the monthly loan payment and the knowledge of how to calculate interest and principal payments.
a. Monthly Payment:
To calculate the monthly payment for a loan, we can use the formula for calculating the fixed monthly payment for a loan:
M = P * (r * (1 + r)^n) / ((1 + r)^n - 1)
Where:
M = Monthly payment
P = Principal loan amount
r = Monthly interest rate (APR divided by 12 months)
n = Number of monthly payments (loan term in years multiplied by 12 months)
Using the given data:
P = $17,500
APR = 12%
n = 20 years
First, let's calculate the monthly interest rate (r):
r = APR / 12 = 0.12 / 12 = 0.01
Next, let's calculate the number of monthly payments (n):
n = 20 years * 12 months/year = 240 months
Now, we can substitute the values into the formula:
M = 17500 * (0.01 * (1 + 0.01)^240) / ((1 + 0.01)^240 - 1)
Calculating this expression will give us the monthly payment amount.
b. Total Amount Paid:
To calculate the total amount paid over the term of the loan, multiply the monthly payment by the number of monthly payments:
Total Amount Paid = Monthly Payment * Number of Monthly Payments
Substituting the values we already calculated will give us the total amount paid.
c. Percentage Paid Toward Principal and Interest:
Now, to determine the percentage paid toward the principal and interest, we need to know the breakdown of each monthly payment. Each payment consists of both principal and interest portions, where the interest is based on the remaining loan balance.
To calculate the interest payment for each month, we can multiply the monthly interest rate (r) by the remaining loan balance. The principal payment for each month is then the monthly payment minus the interest.
To determine the percentage paid toward principal and interest, we'll need to sum up the values for the principal and interest payments over the course of the loan and calculate the respective percentages.
By following these steps and using the given data, you can calculate the monthly payment, total amount paid, and the percentage paid toward principal and interest for the student loan.