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See Example 2.Loans. A student borrowed some money from his father at $2 \%$ simple interest to buy a car. If he paid his father 360 dollars in interest after 3 years, how much did he borrow?
$$\$ 6,000$$
Precalculus
Algebra
Chapter 2
Equations, Inequalities, and Problem Solving
Section 4
Formulas
Algebra Topics That are Reviewed at the Start of the Semester
Equations and Inequalities
Missouri State University
Harvey Mudd College
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and this problem. We're told that a student borrowed money is from his dad at a rate of 2%. And then we were told that he paid his dad $360 in the interest after three years. What we're trying to figure out is how much he borrowed. Well, because we're talking about simple interest, we need to use the equation. I equals P R T. Well, I stands for the interest that's earned. Well, in this case, we were told the interest was $360. That will be our I. The principles would stand for how much he initially borrowed, which is what we're trying to figure out. So what we borrowed is RP. That's our principal. Our ray is 2% that it's getting borrowed, that which we found to be 2%. But remember, we need to turn our percent into a decimal by moving our national two places to the left. So what we find is that our would be equal to 0.2 and then t stands for time, which we're told was three years. So because we're looking for P, what I'm going to do first is Saul my given equation for P. Well, right now he is getting multiplied by our anti Soto. Undo that. I'm going to divide both sides of my equation by our times t So I will be loved with I divided by our times, T is equal to P because they are and the tears will cancel out. Now I simply need to substitute my values into this equation. While our I was 360 our rate was 0.2 and our time was three. So now what we're going to do first is multiply 0.2 times three, which is 30.6 So we'll have 360 divided by 3600.6 and that will be equal to our principal. And now we just need to divide 360 by 3600.6 which we find to be 6000. So what we found is the student would have initially borrowed $6000
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