Questions: Consider the following loan. Complete parts (a)-(c) below. An individual borrowed 64,000 at an APR of 4%, which will be paid off with monthly payments of 346 for 24 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 64000, the annual interest rate is 4% the number of payments per year is 12, the loan term is 24 years, and the payment amount is 346.

Consider the following loan. Complete parts (a)-(c) below.

An individual borrowed 64,000 at an APR of 4%, which will be paid off with monthly payments of 346 for 24 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 64000, the annual interest rate is 4% the number of payments per year is 12, the loan term is 24 years, and the payment amount is 346.

Transcript text: Consider the following loan. Complete parts (a)-(c) below. An individual borrowed $64,000 at an APR of 4%, which will be paid off with monthly payments of $346 for 24 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 $64000, the annual interest rate is $\square$ ere number of payments per year is $\square$ the loan term is $\square$ years, and the payment amount is $ $\square$

Solution

Solution Steps

Step 1: Calculate the Monthly Interest Rate

To find the monthly interest rate, divide the annual rate by 12 and convert it to a decimal. Thus, the monthly interest rate is 0.

Step 2: Calculate the Total Number of Payments

The total number of payments, given 12 payments per year over 24 years, is 288.

Step 3: Calculate the Monthly Payment

Using the formula $M = P \frac{r(1+r)^N}{(1+r)^N - 1}$, where $r$ is 0, $P$ is 64000, and $N$ is 288, the monthly payment is calculated to be $346.04.

Step 4: Calculate the Total Amount Paid

The total amount paid over the term of the loan is the monthly payment multiplied by the total number of payments, which equals $99660.12.

Step 5: Calculate the Percentage Paid Toward Principal and Interest

The percentage of the total amount paid that is allocated towards the principal is 64.22%, and towards the interest is 35.78%.

Final Answer:

The total number of payments is 288, the total amount paid is $99660.12, with 64.22% of the total amount paid allocated towards the principal and 35.78% towards the interest.

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