A loan worth $4500 collects simple interest each year for 12 years. At the end of
that time, a total of $7605 is paid back. Determine the APR for this loan.
Type your answer in the box below. Round your percentage to 2 decimal places.
Your answer should be in the form X.XX%. DO NOT type the %.
could someone help me out i’ve been stuck for awhile and can’t figure it out.
4500(1 + 12r) = 7605
r = 0.0575 or 5.75%
Oh, don't worry, I'm here to help! Let's get clown-y with this math problem.
So, we know that the loan is worth $4500 and it collects simple interest each year for 12 years. At the end of that time, a total of $7605 is paid back.
To find the Annual Percentage Rate (APR), we need to figure out the interest rate. Simple interest is calculated using the formula:
Interest = Principal * Rate * Time
In this case, the Principal is $4500, the Time is 12 years, and the Total Amount paid back is $7605. We're trying to find the Rate, which is the APR we're looking for.
Let's plug in the given values and solve for the Rate:
Interest = $7605 - $4500 = $3105
Principal = $4500
Time = 12 years
Interest = Principal * Rate * Time
$3105 = $4500 * Rate * 12
Now, let's solve for Rate (APR):
Rate = $3105 / ($4500 * 12)
Rate ≈ 0.057
To convert this decimal to a percentage, we multiply it by 100:
Rate ≈ 0.057 * 100
Rate ≈ 5.7%
So, the Annual Percentage Rate (APR) for this loan is approximately 5.7%. Ta-da!
To determine the APR (Annual Percentage Rate) for a loan, we need to use the formula:
Total amount repaid = Principal + (Principal * APR * Time)
Given that the total amount repaid is $7605, the principal is $4500, and the time is 12 years, we can rearrange the formula to find the APR:
APR = (Total amount repaid - Principal) / (Principal * Time)
Substituting the known values into the formula:
APR = ($7605 - $4500) / ($4500 * 12)
Calculating:
APR = $3105 / $54000
APR ≈ 0.0575
Converting to a percentage and rounding to two decimal places:
APR ≈ 5.75%
Therefore, the APR for this loan is approximately 5.75%.
To determine the APR (Annual Percentage Rate) for the loan, we need to use the formula for simple interest:
Simple Interest (SI) = Principal (P) * Rate (R) * Time (T)
Given:
Principal (P) = $4500
Total amount paid back (SI) = $7605
Time (T) = 12 years
We need to find the Rate (R) in order to calculate the APR.
We can rearrange the formula to solve for the rate (R):
Rate (R) = SI / (P * T)
Substituting the given values, we have:
R = $7605 / ($4500 * 12)
R = $7605 / $54,000
R ≈ 0.14125
To convert this into a percentage, multiply by 100:
R ≈ 14.125
Therefore, the APR for this loan is approximately 14.125%.
Please note that APR stands for Annual Percentage Rate, so it represents the yearly interest rate.