Joshua borrowed $1,900 for one year and paid $95 in interest. The bank charged him a service charge of $22. If Joshua paid the $1,900 in 12 equal monthly payments, what is the APR? (Enter your answer as a percent rounded to 1 decimal place.)
So, I got 117/1900= 6.2%, but it says I am wrong.
To calculate the Annual Percentage Rate (APR), you need to consider both the interest paid and the service charge. Here's how you can calculate it step by step:
1. Calculate the total amount paid over one year:
The interest paid is $95, and the service charge is $22. Therefore, the total amount Joshua paid over one year is $95 + $22 = $117.
2. Calculate the monthly payment:
Joshua paid the total amount of $1,900 in 12 equal monthly payments. Therefore, the monthly payment is $1,900 ÷ 12 = $158.33 (rounded to two decimal places).
3. Calculate the annual payment:
Since Joshua made 12 monthly payments, multiply the monthly payment by 12: $158.33 × 12 = $1,900.
4. Calculate the APR:
The APR can be found by dividing the total amount paid over one year by the loan amount and then multiplying by 100:
APR = ($117 ÷ $1,900) × 100 = 6.1579% (rounded to four decimal places)
Therefore, the APR is approximately 6.2% when rounded to one decimal place. It seems your answer is correct, so please double-check your calculations.
To calculate the Annual Percentage Rate (APR), you need to consider both the interest paid and the service charge. Here's how you can calculate the APR step by step:
Step 1: Determine the total amount paid over the year.
The total amount paid can be calculated by adding the borrowed amount ($1,900) to the total interest paid ($95) and the service charge ($22):
Total amount paid = Borrowed amount + Interest + Service charge
Total amount paid = $1,900 + $95 + $22
Total amount paid = $2,017
Step 2: Calculate the monthly payment.
Since Joshua paid $1,900 in 12 equal monthly payments, the monthly payment amount can be calculated by dividing the total amount paid by 12:
Monthly payment = Total amount paid / Number of months
Monthly payment = $2,017 / 12
Monthly payment = $168.08 (rounded to two decimal places)
Step 3: Calculate the monthly interest rate.
To find the monthly interest rate, divide the total interest paid by the borrowed amount and divide by 12 (since there are 12 months in a year):
Monthly interest rate = (Total interest paid / Borrowed amount) / Number of months
Monthly interest rate = ($95 / $1,900) / 12
Monthly interest rate = 0.005 / 12
Monthly interest rate ≈ 0.00042 (rounded to five decimal places)
Step 4: Convert the monthly interest rate to an annual interest rate (APR).
To find the APR, multiply the monthly interest rate by 12 to get the annual interest rate:
APR = Monthly interest rate * 12 * 100
APR = 0.00042 * 12 * 100
APR ≈ 0.504% (rounded to one decimal place)
Therefore, the APR for Joshua's loan is approximately 0.5%.
try that answer..? lol
95/ 1900
= 0.05 ---> 5%