Jean purchased a $995 stereo system on the installment plan. She paid
20% down. The finance charge on the remainder was 19.4%. She was
given 18 months to pay off the balance. What was her monthly payment?
The original unpaid balance was
P = 0.8 x 995 = $796.00
A finance charge of 19.4% is 19.4%/12 = i = 1.61667% per month. The number of payments is n = 18
The formula you need to use can be found at
http://en.wikipedia.org/wiki/Amortization_calculator
It is
A = P i /[1 - (1+i)^-n]
In your case,
A = 796*.0161667/[1 - 0.74929] = $51.32
To find Jean's monthly payment, we need to calculate the amount she borrowed (the remainder after the down payment) and then divide it by the number of months she has to pay it off.
Step 1: Calculate the down payment.
Jean paid 20% down on a $995 stereo system.
Down payment = 20% of $995 = 0.20 * $995 = $199
Step 2: Calculate the amount borrowed.
The remaining amount is the original price minus the down payment.
Amount borrowed = $995 - $199 = $796
Step 3: Calculate the finance charge.
The finance charge is 19.4% of the amount borrowed.
Finance charge = 19.4% of $796 = 0.194 * $796 = $154.624
Step 4: Calculate the total amount to be paid back.
Total amount to be paid back = Amount borrowed + Finance charge
Total amount to be paid back = $796 + $154.624 = $950.624
Step 5: Calculate the monthly payment.
The monthly payment is the total amount to be paid back divided by the number of months.
Monthly payment = Total amount to be paid back / Number of months
Monthly payment = $950.624 / 18 months = $52.81 (rounded to the nearest cent)
Therefore, Jean's monthly payment is $52.81.
To find the monthly payment, we need to calculate the total amount Jean needs to pay. Let's break it down step by step:
1. Calculate the down payment:
Since Jean paid 20% down on the stereo system, we can calculate the down payment amount:
Down payment = 20% of $995
= 0.20 * $995
= $199
2. Calculate the remaining balance:
To find the remaining balance, subtract the down payment from the total cost:
Remaining balance = Total cost - Down payment
= $995 - $199
= $796
3. Calculate the finance charge:
The finance charge is given as 19.4% of the remaining balance:
Finance charge = 19.4% of $796
= 0.194 * $796
= $154.424
4. Calculate the total amount to be paid:
The total amount to be paid is the sum of the remaining balance and the finance charge:
Total amount = Remaining balance + Finance charge
= $796 + $154.424
= $950.424
5. Calculate the monthly payment:
Now that we have the total amount to be paid and the duration, we can calculate the monthly payment using the formula for an installment plan:
Monthly payment = Total amount / Number of months
= $950.424 / 18
≈ $52.80 (rounded to nearest cent)
So, Jean's monthly payment for the stereo system on the installment plan is approximately $52.80.