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.

cost = 300 + 40(1 - 1.0325^-24)/.0325

= $ 959.53

interest paid = 300 + 24(40) - 959.53 = $300.47

Wow, that is 39% . Is that even legal?
In the middle ages they would have burned you at the stake for usury.

Thank you so much for this. And I really like the way you lay out the way it is solved. easy to understand.

To solve this problem, we can follow these steps:

Step 1: Calculate the cost of the stereo.

The cost of the stereo can be calculated by adding the down payment to the total monthly payments over the next 2 years.

Down payment: $300
Monthly payment: $40
Number of months: 2 years, which is equal to 2 years * 12 months/year = 24 months

Cost of the stereo = Down payment + (Monthly payment × Number of months)

Cost of the stereo = $300 + ($40 × 24)
Cost of the stereo = $300 + $960
Cost of the stereo = $1260

So, the cost of the stereo is $1260.

Step 2: Calculate the total amount of interest paid.

The interest rate per month is given as 3.25%. To calculate the interest paid each month, we need to multiply the outstanding balance (which decreases each month) by the interest rate. Then we can sum the interest paid for all the months to get the total interest paid over the 2-year period.

To find the outstanding balance each month, we can subtract the cumulative payments made until that month from the total cost of the stereo.

Outstanding balance after month n = Cost of the stereo - (Monthly payment × n)

Interest paid each month = Outstanding balance × Interest rate

To find the total interest paid, we need to sum the interest paid for each month.

Total interest paid = Interest paid month 1 + Interest paid month 2 + ... + Interest paid month 24

Let's calculate:

Outstanding balance after month 1 = $1260 - ($40 × 1) = $1260 - $40 = $1220
Interest paid month 1 = $1220 × 0.0325 = $39.65

Outstanding balance after month 2 = $1260 - ($40 × 2) = $1260 - $80 = $1180
Interest paid month 2 = $1180 × 0.0325 = $38.35

Continue these calculations for all 24 months and sum them up:

Total interest paid = $39.65 + $38.35 + ... + interest paid month 24

I can help calculate this sum if you would like.

To find the cost of the stereo, you can add the initial down payment to the total amount paid in monthly installments. Let's break down the process step by step:

a) The cost of the stereo:
1. First, calculate the total amount of monthly payments over the next 2 years (24 months): $40/month x 24 months = $960.
2. Add the down payment of $300 to the total monthly payments: $960 + $300 = $1260.
3. Therefore, the cost of the stereo is $1260.

b) The total amount of interest paid:
1. Calculate the monthly interest rate by dividing the annual interest rate (3.25%) by 12: 3.25% / 12 = 0.27083% per month (rounded to 5 decimal places).
2. Calculate the total interest paid over the 2-year period by multiplying the monthly interest rate by the number of months (24 months): 0.27083% * 24 = 6.5% (rounded to 1 decimal place).
3. Calculate the total interest amount by multiplying the cost of the stereo by the percentage: $1260 * 6.5% = $81.90.

Therefore:
a) The cost of the stereo system is $1260.
b) The total amount of interest paid is $81.90.

Hope this helps! Let me know if you have any further questions.