Stereo Inc. sells a stereo system for $300 down and monthly payments of $40 for the next 2 years. If the interest rate is 3.25% per month, find:
a) The cost of the stereo.
b) The total amount of interest paid.
I am having trouble figuring out the correct layout.
No worries! Let me break down the calculation for you.
a) To find the cost of the stereo system, you need to add the down payment to the total of the monthly payments over the course of 2 years.
The down payment is given as $300.
The monthly payment is $40 for 2 years, which means there are a total of 24 monthly payments (12 months/year × 2 years).
To calculate the total of the monthly payments, multiply the monthly payment amount by the number of payments:
Total monthly payments = $40/month × 24 months
Now, to find the cost of the stereo system, add the down payment to the total of the monthly payments:
Cost of stereo system = Down payment + Total monthly payments
b) To calculate the total amount of interest paid, you need to find the interest paid on each monthly payment and then sum them up.
The interest rate is given as 3.25% per month. Since the payments are made monthly, the interest is compounded monthly.
To find the interest paid for each monthly payment, multiply the remaining balance of the stereo system by the interest rate:
Interest paid for each monthly payment = Remaining balance × Interest rate
For the first monthly payment, the remaining balance is the cost of the stereo system. However, for each subsequent monthly payment, the remaining balance will decrease.
To calculate the remaining balance for each monthly payment, subtract the amount paid from the previous month's remaining balance.
To calculate the total amount of interest paid, sum up the interest paid for each monthly payment.
Here's how you can calculate it step-by-step.