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Question 1083543: A business owner takes on a $8,000 loan to cover expenses. The interest rate on the loan is 3% per year. Each year, the business owner pays $500 toward the loan. Find the balance on the loan after the third payment is made (round your answer to the nearest cent).
A) $7,472.20
B) $7,196.37
C) $6,912.26
D) $7,740.00
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
Answer: Choice B) $7,196.37
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Explanation:
Let's walk through each of the three years.
What I'm focused on are three things
- the interest paid
- the principal paid
- the remaining balance
The most important is the remaining balance as the last remaining balance (for year 3) will be the final answer.
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Let's start the walk through. Everything but the interest rate are values in dollars.
Year 1:
interest paid = (interest rate in decimal form)*(current balance)
interest paid = (0.03)*(8000)
interest paid = 240
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principal paid = (payment amount) - (interest paid)
principal paid = (500) - (240)
principal paid = 260
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new balance = (old balance) - (principal paid)
new balance = (8000) - (260)
new balance = 7740
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Year 2:
interest paid = (interest rate in decimal form)*(current balance)
interest paid = (0.03)*(7740)
interest paid = 232.2
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principal paid = (payment amount) - (interest paid)
principal paid = (500) - (232.2)
principal paid = 267.8
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new balance = (old balance) - (principal paid)
new balance = (7740) - (267.8)
new balance = 7472.2
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Year 3:
interest paid = (interest rate in decimal form)*(current balance)
interest paid = (0.03)*(7472.2)
interest paid = 224.166
interest paid = 224.17 round to the nearest penny
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principal paid = (payment amount) - (interest paid)
principal paid = (500) - (224.17)
principal paid = 275.83
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new balance = (old balance) - (principal paid)
new balance = (7472.2) - (275.83)
new balance = 7196.37
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The third payment has been made, so we can stop.
This is why the answer is $7,196.37
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Extra Info (Optional):
If you wish, you can create a table such as this one
which will display all of the relevant data in a compact format.
Each of the values in the table can be found above (in the walkthrough).
Take note how columns B and C add up to the payment ($500)
The answer is highlighted.
The table was created with Microsoft Excel but other alternatives (such as the spreadsheet program from OpenOffice or LibreOffice) will get the job done as well.
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