To the nearest dollar, how much money needs to be invested in an accou

Question

To the nearest dollar, how much money needs to be invested in an account that earns 8 % interest, compounded quarterly, in order to have $12,000 at the end of 3 years?

(A) $9,462

(B) $9,326

(C) $9,677

(D) $9,804

(E) $11,308

GMATinsight · Answer

Amount = Principal  ^n

Number of Compounding in 3 years = 3*4 = 12
Interest rate per compounding = 8/4 = 2

i.e.  12000 = P  ^{3*4}

P = 9461.9 = 9462

Answer: option A

But this method can't be applied in GMAT so I would be curious to find how will others solve it without such calculations.

US09 · Answer

Is there a short cut to the traditional A=P(1 +R/100)^T method? Also, I got confused as there was no "per annum" mentioned after 8%. So, if nothing is mentioned do we assume the rate of interest is annual only? I know this is a dumb question but I just want to be sure for GMAT.

generis · Answer

urvashis09 , your question is not dumb! You wanted to be sure. You explained the issue and asked a specific question. That is exactly how to ask a good question. Although the prompt does not say 8% per annum, the word "quarterly," unless explicitly defined otherwise in an interest problem on the GMAT, means four times per year . (I have never seen an interest rate "compounded quarterly" defined in way.) Further, the question asks about the end of 3 years . From that term you can also safely assume that you are dealing with a yearly rate, compounded quarterly. Re: shortcut . . . Not that I know of. Estimation in a strict sense will not work here; the answer values are too close together. But there are other ways to think about the issue presented. . . Hope that helps.

US09 · Answer

Oh, now I get it. I was reading every word way too closely, missing out on the meaning of the entire sentence. Thank you for the explanation!

Shobhit7 · Answer

At Simple Interest of 8%pa,
Three years of interest amount to 24%

So, if principal amount is P,
After three years, Final amount is 1.24P

Equating, 1.24P=12000
P=9677

Hence, correct answer must be below 9677.

So, probable answers are A&B.

In such a case, an educated guess should be a value smaller than and closed to 9677.

This boils down to Ans A.

IMO, this is the fastest way to estimate an answer.

Posted from my mobile device

generis · Answer

I have a hunch that the multiplier can be
found with the    binomial theorem.

We have two terms raised to a heinous power from the compound interest formula:

A = P(1 + \frac{r}{n})^{nt} 
In which
 A  = $12,000
 P  = the number we need, Principal
 r = Rate in decimal form
 n  = # of pay periods per year
 t  = time

r =.08 
 n = 4 
 t = 3 
 \frac{r}{n} = \frac{.08}{4} = .02  
 (1 + .02)^{12} = ?

Just a thought . . .

PRI23YA · Answer

I could get the answer using the calculator, but was slightly lost solving the last step.

Is there a way we can find out x*(1.02)^12=12000 in the test?

KarishmaB   Bunuel , do you mind helping us with this? Thank you.

To the nearest dollar, how much money needs to be invested in an accou

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To the nearest dollar, how much money needs to be invested in an accou

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