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# How much did he borrow?

A student borrowed some money from his father at 2% simple interest to buy a car. If he paid his father \$360 in interest after 3 years, how much did he borrow?

Okay Lucy this is the equation for simple interest:

P * R = I

where:

P = principle or amount borrowed

R = rate of interest per term (which in this case appears to be annual)

I = Interest per term (which in this case appears to be annual)

Since it is simple interest the principle is constant.

So \$360/3 years = \$120 per year which is 2% of the principle per year

therefore from the equation we rearrange to get:

P = I/R

so P = \$120/0.02  = \$6000  (remember the decimal equivalent of the rate of interest)

each year he paid 2% of \$6000 or a total amount of 6% of \$6000 for a total of 0.06(\$6000) = \$360

Now you want to know how much he borrowed which would be the principle of \$6000.

Hope this helps!

Art

Hi Lucy,

Let's first look at how interest works.

If I borrow \$1000 from you at 5% interest per year, after 1 year I will have to pay you \$1000 plus 5% of \$1000.  Now, 5% means 5/100, so 5% of \$1000 is 5/100 times 1000, which is 5 times 1000/100 which is 5 times 10 = \$50.  So after 1 year I would have to pay you back \$1000 plus \$50, which is \$1050.

After 2 years, I would have to pay you \$1000 plus \$50 for the 1st year plus \$50 for the 2nd year, which would be \$1100.

So the interest I owe you would be the loan amount (\$1000) times the interest rate (5%, or 5/100) times the time (2 years).

In your problem, we know the interest, the interest rate, and the time.  So we would say that the interest (\$360) is equal to the loan amount (unknown) times the interest rate (2%, or 2/100) times the time (3 years).  At this point, we have to do a little algebra:

360 = 2 * 3 * x / 100

The opposite of dividing by 100 is multiplying by 100, so

360 * 100 = 2 * 3 * x,

36000 = 6x   (divide both sides by 6)

x = 6000.

The student borrowed \$6000 from his father and bought a very reliable, cheap used car, or maybe a fancy, but not very dependable pre-owned car!

Hi Lucy.

You can use the simple interest formula to solve this. I=Prt

We know the interest (I), the rate (r) and the time (3) with the principal (P) as the variable, so the equation looks like this: 360=P(.02)(3)

360=P(.06)

360/.06=P

P=\$6,000

When you know the formula, this kind of problem is easy! Best of luck to you!