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A $2000 investment is compounded 2 times annually

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by vinni.k » Fri Dec 07, 2012 6:05 am
A $2000 investment is compounded 2 times annually at an annual rate of x% If the final investment is worth $3380 after 1 year, what is the rate?
A. 30%
B. 56%
C. 60%
D. 69%
E. 73%

Answer is C

My answer is D. I am not sure where i am making the mistake. I am applying the right formula of compound interest. I am taking r/100 in the formula P(1 + r)^n
Is that wrong ? I have seen questions in which "r" is used as P(1 + .10)^n
I can convert .10 into 10/100.

Looking forward to your replies.

Thanks & Regards
Vinni
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by GMATGuruNY » Fri Dec 07, 2012 7:30 am
vinni.k wrote:A $2000 investment is compounded 2 times annually at an annual rate of x% If the final investment is worth $3380 after 1 year, what is the rate?
A. 30%
B. 56%
C. 60%
D. 69%
E. 73%

Answer is C
We can plug in the answers, which represent the interest rate.
Since the rate is COMPOUNDED two times, 1/2 of the rate is applied after the first period, with the remaining 1/2 applied at the end of the second period.
Since the final amount is an INTEGER, the interest rate is almost certainly a MULTIPLE OF 10.

Answer choice C: 60%
2000 + .3(2000) = 2000 + 600 = 2600.
2600 + .3(2600) = 2600 + 780 = 3380.
Success!

The correct answer is C.
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by vinni.k » Fri Dec 07, 2012 10:14 am
GMATGuruNY wrote:
We can plug in the answers, which represent the interest rate.
Since the rate is COMPOUNDED two times, 1/2 of the rate is applied after the first period, with the remaining 1/2 applied at the end of the second period.
Since the final amount is an INTEGER, the interest rate is almost certainly a MULTIPLE OF 10.

Answer choice C: 60%
2000 + .3(2000) = 2000 + 600 = 2600.
2600 + .3(2600) = 2600 + 780 = 3380.
Success!

The correct answer is C.
Thanks Mitch :D

Regards
Vinni
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by ziko » Tue Dec 11, 2012 5:16 am
Method suggested above is briliant but for me sometimes its better to work with equations.
So 2000*x^2=3380; x^2=338/200, x=13/10.
Now we need to answer what is x? x=1+x/100=(100+x)/100 now replace with what we have for x and we get the following equation: 13/10=(100+x)/100; this leads us that x=30, considering that 30 is the interest rate for 6 months annual interest rate will be 30*2=60

So answer is 60%
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