You buy furniture for $700. The retailer finances the entire amount for one year and says you will be charged 9% interest. The retailer uses the add-on method. Assuming your first monthly payment is due in one month, calculate the real annual rate you will pay.
Using this weird method, monthly payment = (700 + 700(.09)(1)/12 = 763/12 = 63.58
let the real monthly rate be x
63.58(1 - (1+x)^-12)/x = 700
this type of equation is very messy to solve, so let's go to Wolfram
https://www.wolframalpha.com/input/?i=solve+63.58(1+-+(1%2Bx)%5E-12)%2Fx+%3D+700
to get x = .0135054
annual rate = .162...
or appr 16.2%, quite a bit more than the stated 9%
To calculate the real annual rate you will pay, we need to consider the add-on interest method. The add-on interest method calculates the interest as a percentage of the original loan amount.
First, let's determine the interest charged for the one-year loan:
Interest = Loan Amount x Interest Rate
Interest = $700 x 9% = $63
Now, let's calculate the total amount you will need to repay:
Total Amount = Loan Amount + Interest
Total Amount = $700 + $63 = $763
Since you will be making monthly payments, multiply the total amount by 12 (number of months in a year) to determine the annual repayment amount:
Annual Repayment Amount = Total Amount x 12
Annual Repayment Amount = $763 x 12 = $9156
Finally, we can calculate the real annual rate you will pay using the following formula:
Real Annual Rate = (Annual Repayment Amount - Loan Amount) / Loan Amount * 100
Real Annual Rate = ($9156 - $700) / $700 * 100
Real Annual Rate = $8456 / $700 * 100
Real Annual Rate = 1208%
Therefore, the real annual rate you will pay is 1208%.
To calculate the real annual rate you will pay, we first need to understand the add-on method.
In the add-on method, the interest is calculated based on the original principal amount and added to the total loan amount. Then, the total is divided by the number of payments to determine the installment amount.
In this case, the furniture costs $700, and you will be charged 9% interest for one year.
To calculate the interest amount, we can multiply the principal ($700) by the interest rate (9% or 0.09):
Interest = $700 * 0.09 = $63
The total amount you will have to repay, including interest, is the principal plus the interest:
Total repayment = $700 + $63 = $763
Since the loan is for one year, there will be twelve monthly payments. So, we divide the total repayment amount by the number of payments to get the monthly installment:
Monthly installment = $763 / 12 = $63.58
Finally, to calculate the real annual rate you will pay, divide the total interest ($63) by the principal ($700), and multiply by 100 to express it as a percentage:
Real annual rate = ($63 / $700) * 100 = 9%
Therefore, the real annual rate you will pay using the add-on method is 9%.