SOLUTION: Linda took out a simple interest loan for $7,000 at 11% interest for 5 years. How much interest did she have to pay back?

Question 496044: Linda took out a simple interest loan for $7,000 at 11% interest for 5 years. How much interest did she have to pay back?
Found 2 solutions by lmeeks54, MathTherapy:
Answer by lmeeks54(111) (Show Source): You can put this solution on YOUR website!
This is another common type of question designed to teach the student how to perform a straight forward task (e.g., calculate the amount of interest paid based upon some given values); however, it is of only limited utility to the "real person" because the "real world" is a little more complex.
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I will answer the question asked, and then provide some bonus information about how these kinds of problems more commonly work in the "real world."
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Givens:
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Principal = 7,000
Interest = 11%
Term is = 5 years
Interest is simple interest (vs. compound interest)
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To calculate the total amount of interest, simply multiply the simple interest rate x the present value (starting value) of the loan (also called its principal):
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7,000 x 11% (or .11) = 770
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Q. What is the total interest? A. 770
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Two things are more useful to know for most borrowers:
-- what is my payment?
-- is this all I have to pay?
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To calculate the monthly payment from the original question above, sum the original principal and the total interest to be paid, and then divide by the number of months for the term of the loan.
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The original question didn't ask for the monthly payment, so the value given for the term of the loan (5 years, which we convert to 60 months) is useless for the original problem, but is necessary when calculating the payment.
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Loan Principal ... 7,000
Total interest ... + 770
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Total to repay ... 7,770
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7,770 / 60 months = 129.50/month
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This is useful to know since more people worry about affording their monthly payment than they do knowing their total interest to be paid.
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But there is more. Most consumer loans are compound interest loans and not simple interest loans. The type of loan is important because compound interest loans are ALWAYS more expensive for the consumer, if all other factors are equal. They are harder to figure out too, thus many people believe only bankers and accountants can compute payments and total interest paid on compound interest loans. But that is not true. Read on...
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Simple interest loans are simple because the total interest is a function of the interest rate and the original principal. The payment is easy to figure out too, as we saw above: divide the total owed by the number of payments (usually the number of months).
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Compound interest problems are complicated by fact that interest owed is a function of both the interest rate and loan principal, as before, but also takes into account time as a factor. That is, the longer the loan is open (time until all interest and principal are repaid), the longer the interest accrues. The interest part of the monthly payment varies over time. Normally, as time goes on and principal is paid down, the interest on the remaining principal goes down too.
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The interest going down part is interesting (and sounds good for the borrower); however, it starts out much higher for the borrower at the beginning of the loan.
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Consider the original problem:
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7,000 principal, 11% int rate, 5 year loan, simple interest: monthly payment is 129.50 and the total interest is 770.
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If this were a zero interest loan, we would have multiplied 0% x 7,000 and gotten -0- as the total interest, and we would have divided 7,000 (and not 7,770) by 60 to get a monthly payment of 116.67. That means the principal payment part of the problem is 116.67/month for 60 months. That's only 12.83 in interest in our monthly payment at the 11% simple interest problem.
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If this were a 11% compound interest problem, taking into account the 5 year term of the loan, the monthly payment would be 152.20. Over the course of the 60 month loan, the total interest would be 2,132, almost 3 times the total interest in the simple interest problem!
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Normally a calculator or a computer (e.g., MS Excel) is required to calculate a loan amortization table (a table of all monthly payments, including the decreasing principal balance and decreasing part of the total payment going to interest). But the problems are VERY easy to set up.
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More later,
Lee
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Linda took out a simple interest loan for $7,000 at 11% interest for 5 years. How much interest did she have to pay back?

Simple interest = PTR, where P = principal or amount of loan, T = time (in years), and R = interest rate (annual)

We therefore have: Simple interest = (7,000)(5)(.11) ----- $

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