Questions: Consider the following loan. Complete parts (a)-(c) below.
An individual borrowed 81,000 at an APR of 3%, which will be paid off with monthly payments of 384 for 25 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is 81000, the annual interest rate is 3%, the number of payments per year is 12, the loan term is 25 years, and the payment amount is 384.
b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?
There are 300 payments toward the loan and the total amount paid is 115200.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?
The percentage paid toward the principal is (Round to the nearest tenth as needed.)
%.
Transcript text: Consider the following loan. Complete parts (a)-(c) below.
An individual borrowed $\$ 81,000$ at an APR of $3 \%$, which will be paid off with monthly payments of $\$ 384$ for 25 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is $\$ 81000$, the annual interest rate is $3 \%$, the number of payments per year is 12 , the loan term is 25 years, and the payment amount is $\$ 384$.
b. How many total payments does the loan require? What is the total amount paid over the full term of the loan?
There are 300 payments toward the loan and the total amount paid is $\$ 115200$.
c. Of the total amount paid, what percentage is paid toward the principal and what percentage is paid for interest?
The percentage paid toward the principal is $\square$ (Round to the nearest tenth as needed.)
$\square$ \%.
Solution
Solution Steps
Step 1: Calculate the Monthly Payment
To calculate the monthly payment, we use the formula:
\[ M = P \frac{r(1+r)^n}{(1+r)^n - 1} \]
Where:
\( P = 81000 \) (the loan principal),
\( r = 0.0025 \) (the monthly interest rate),
\( n = 300 \) (the total number of payments).
Plugging in the values, we get:
\[ M = 384.1 \]
Step 2: Calculate the Total Amount Paid Over the Term of the Loan
The total amount paid over the term of the loan is calculated as:
\[ \text{Total Paid} = M \times n = 384.1 \times 300 = 115233.3 \]
Step 3: Calculate the Distribution of Payments Between Principal and Interest
The total interest paid over the term of the loan is:
\[ \text{Total Interest} = \text{Total Paid} - P = 115233.3 - 81000 = 34233.3 \]
The percentage paid towards the principal is:
\[ \frac{P}{\text{Total Paid}} \times 100\% = 70.3\% \]
The percentage paid for interest is:
\[ \frac{\text{Total Interest}}{\text{Total Paid}} \times 100\% = 29.7\% \]
Final Answer:
The monthly payment is \( 384.1 \), the total amount paid over the term of the loan is \( 115233.3 \),
with \( 70.3\% \) of the payments going towards the principal and \( 29.7\% \) towards interest.