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determine the cost of credit for a $3,300 loan with a simple interest rate of 8% and a one time payment to pay the amount in full at the end of a 4-year term. Round the answer to two decimal places as needed

5 answers

To determine the cost of credit for a loan with simple interest, you can use the formula for simple interest:

\[ I = P \times r \times t \]

Where:

  • \( I \) is the interest paid.
  • \( P \) is the principal amount (the initial loan amount).
  • \( r \) is the annual interest rate (as a decimal).
  • \( t \) is the time in years.

Here, you provided:

  • \( P = 3300 \)
  • \( r = 8% = 0.08 \)
  • \( t = 4 \)

Plugging in these values:

\[ I = 3300 \times 0.08 \times 4 \]

Calculating:

\[ I = 3300 \times 0.08 = 264 \] \[ I = 264 \times 4 = 1056 \]

So, the total interest paid over the 4 years is $1,056.

To find the total cost of the loan (the amount paid back), add the interest to the principal:

\[ \text{Total Cost} = P + I = 3300 + 1056 = 4356 \]

Thus, the total cost of credit, which includes both the principal and the interest, is:

\[ \text{Total Cost} = 4356 \]

Rounded to two decimal places, the cost of credit for the loan is $4,356.00.

The 1,056 is correct.
Next, determine the cost of credit for a 2-year, $5,000 credit car loan with a monthly payment of $257.67, which corresponds to a fixed compund interest rate of a 21.3% compounded monthly. Round the answer to 2 decimal places as needed.

To calculate the cost of credit for the credit card loan, we can follow these steps:

  1. Determine the total amount paid over the term of the loan.
  2. Subtract the principal from the total amount paid to find the cost of credit (interest paid).

Step 1: Total Amount Paid

The loan is for 2 years, and the monthly payment is $257.67. Let's calculate the total number of payments and the total amount paid.

  • Number of months in 2 years = \( 2 \times 12 = 24 \)

Now we can calculate the total amount paid over the life of the loan:

\[ \text{Total Amount Paid} = \text{Monthly Payment} \times \text{Number of Months} = 257.67 \times 24 \]

\[ \text{Total Amount Paid} = 6,184.08 \]

Step 2: Calculate the Cost of Credit

The principal amount is $5,000, so we can find the cost of credit (interest paid):

\[ \text{Cost of Credit} = \text{Total Amount Paid} - \text{Principal} = 6,184.08 - 5,000 \]

\[ \text{Cost of Credit} = 1,184.08 \]

Final Result

The cost of credit for the 2-year, $5,000 credit card loan is:

\[ \text{Cost of Credit} = \text{$1,184.08} \]

Rounded to two decimal places, the final answer is $1,184.08.

Correct.

Great! I'm glad the calculations were correct. If you have any more questions or need further assistance, feel free to ask!