FDP question bank #3

[maolivie]

Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?

$1500
$1750
$2000
$2500
$3000

according to the explanation:

You can solve this problem without using compound interest. 8% interest over half a year, however that interest is compounded, is approximately 4% interest. So, to compute the principal, it's actually a very simple calculation:

100 = .04x
2500 = x

The correct answer is D.

what happened to the addition of 1 in the compounding interest equation. Shouldn't it be 1.04x=100?

[Guest]

hi
i don't know where you got your eqn from, but the eqn for interest is: i = Prt.

100 = P(.04)(1)
P = 10,000/4
P = 2500

hope that helps!

[dbernst]

That is correct. In this problem, the most logical approach is to use the interest formula I = (P)(r)(t), or
100 = P(.04)(1).

The greater takeaway from this problem is the use of the word "approximately." When a problem on the GMAT specifically states "approximately," the test makers are telling you there is no reason to solve using an exact but lengthy process. Instead, use skills such as rounding, ballparking, and strategic guessing to quickly eliminate the four incorrect answer choices.

-Dan

[kramacha1979]

Can someone help me solve the problem using the traditional Compound Interest formula

A = P( 1+ r/100) ^ nt

A = X+ 100
P = X

R = 8
N = 4
T = 0.5.

I don't get P = X = 2500. What am I doing wrong?

[jnelson0612]

Can someone help me solve the problem using the traditional Compound Interest formula

A = P( 1+ r/100) ^ nt

A = X+ 100
P = X

R = 8
N = 4
T = 0.5.

I don't get P = X = 2500. What am I doing wrong?

I think something is wrong with your formula. For example, if I have invested $100 and am getting 8 percent interest, compounded quarterly, for one year, the principal and interest at the end of the year should be about $109-$110. If I use your formula I get 100(1.08)^4. That would equal $136.04. It should actually be 1.02 that is taken to the 4th power (and of course divided by 2). Please verify your formula.