Problem Solving

A car loan is offered a 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?

I think I approach this problem this way

P(1+.08) = 240
240/(1.08) =222.2

This however, is not the correct answer.

The answer is 3,000
I know the formula for compound interest is P(1+r/n)^nt

Please assist.

The right side of your equation should be principal plus interest.

P(1 + .08) = P + 240

1.08P = P + 240

.08P = 240

P = 3000

sanchu wrote:A car loan is offered a 8% annual interest, compounded annually. After the first year, the interest due is $240. What is the principal on the loan?

1000
3000
4000
5000
6000

I've added answer choices, which the GMAT would provide.

Keep it simple.
Since the interest is compounded annually, the interest starts to be compounded only AFTER the first year.
Thus, the $240 earned during the first year is NOT compounded and thus is simply 8% of the principal:
240 = (8/100)x
x = 24000/8 = 3000.

The correct answer is B.

An alternate approach is to PLUG IN THE ANSWERS, which represent the principal.
8% of the correct answer choice must yield $240 in interest.

Answer choice C: 4000
(8/100)(4000) = 320.
The correct answer must be smaller.
Eliminate C, D and E.

Answer choice B: 3000
(8/100)(3000) = 240.
Success!

The correct answer is B.

Why do I need to write P + 240 on the right side of the equation?

If you do it Mitch's way, you don't, but in your equation, you had principle multiplied interest on the left, so the right side should be principal plus interest.

If you look at my second step:

1.08P = P + 240

The principle, plus another 8 percent of the principal, is equal to the principal plus 240. Thus, 240 is equal to 8 percent of the principal.