what formula did the book use and the set up for it to get this answer for this problem:
Problem:
Stereo shack sells a stereo system for $600 down and monthly payments of $30 for the next 3 yrs. In the interest rate is 1.25% per month on the unpaid balance, find the cost of the stereo system.
Answer:
$1465.42
The amount of loan that gets amortized at $30 a month and 1.25% monthly interest is $865.42. Add the down payment to that and you get the original price.
You will need an amortization table such as http://ray.met.fsu.edu/cgi-bin/amortize
To arrive at the answer of $1465.42, the book likely used an amortization table or a similar method. Here's how you can set it up to get the answer:
The problem states that the stereo system is sold for $600 down and monthly payments of $30 for the next 3 years. The interest rate is given as 1.25% per month.
To find the cost of the stereo system, you need to calculate the unpaid balance after the 3 years and then add the down payment to it.
Here's how to set up the calculation:
1. Calculate the total number of payments: Since the term is 3 years and there are 12 months in a year, the total number of payments is 3 x 12 = 36 payments.
2. Determine the monthly interest rate: The interest rate is given as 1.25% per month. To convert it into a decimal, divide it by 100. So, the monthly interest rate is 1.25/100 = 0.0125.
3. Calculate the monthly payment towards the principal: Since the monthly payments are $30, subtract the monthly interest from this to find the payment towards the principal. In this case, it would be $30 - (0.0125 * unpaid balance).
4. Set up an amortization table: You can use an online amortization table generator, like the one mentioned in the problem (http://ray.met.fsu.edu/cgi-bin/amortize), or a spreadsheet software like Excel.
In the amortization table, enter the following variables:
- Loan Amount: $600
- Annual Interest Rate: 1.25%
- Loan Term: 3 years or 36 months
The amortization table will provide a breakdown of each monthly payment, including the portion going towards interest, the portion going towards principal, and the remaining balance.
5. Calculate the unpaid balance after 3 years: Look at the final entry in the amortization table for the remaining balance. In this case, it would be $865.42.
6. Add the down payment: Finally, add the down payment of $600 to the unpaid balance to obtain the cost of the stereo system, which is $1465.42.
Note: The exact formula used in the book to derive the answer may vary based on the specific method or approach utilized. However, the general principles of calculating the unpaid balance and adding the down payment remain the same.