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vidhimistry: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Fri Apr 22, 2011 1:43 pm

by vidhimistry » Tue Apr 26, 2011 5:36 am

A 2-year certificate of deposit is purchased for k dollars. If the certificate earns interest at an annual rate of 6 percent compounded quarterly, which of the following represents the value, in dollars, of the certificate at the end of the 2 years ?

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Source: Beat The GMAT — Problem Solving | Tue Apr 26, 2011 5:36 am

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by GMATGuruNY » Tue Apr 26, 2011 5:55 am

vidhimistry wrote:A 2-year certificate of deposit is purchased for k dollars. If the certificate earns interest at an annual rate of 6 percent compounded quarterly, which of the following represents the value, in dollars, of the certificate at the end of the 2 years ?

The formula for repeated percent change in which a value is repeatedly increased by r%:

Final amount = Original Amount * (1 + r/100)^number of changes.

In the problem above:
Original amount = k.
r = 6/4 = 1.5. (Every quarter the certificate receives 1/4 of the 6 percent interest.)
Number of changes in 2 years = 8. (Every quarter for 2 years = 4*2 = 8 changes).

Thus:
Final amount = k*(1 + 1.5/100)â�¸ = k*(1.015)â�¸.

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Tue Apr 26, 2011 6:46 am

I got a different formula, where am I wrong?

K * (1 + i)^n

i = interest rate. Because 6% is anually we must convert it to a quaterly interest rate. Because there are "three" quaters in a year (3 * 4Q = 12) , then we must divide the interest rate by 3. So instead of 0.06 we should use 0.02

n = # capitalizations. If in one year there are 3 quaters, in two years there should be 6 quaters. So we must use n = 6 to calculate compound interest 6 times.

Putting it all together:

K *(1+0.02)^6
K *(1.02)^6

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pankajks2010: Master | Next Rank: 500 Posts; Posts: 118; Joined: Wed Mar 16, 2011 12:51 amFollowed by: 1 member; Location: New Delhi, India; Thanked: 12 times

by pankajks2010 » Tue Apr 26, 2011 9:25 am

In a year there are 4 quarters and every quarter has 3 months.

Thus, the annual interest rate would get divided by 4 and not 3.

Similarly, the time period (n) would become 2*4=8 and not 6.

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Tue Apr 26, 2011 10:05 am

Oh now I see... it's a bit different in spanish...

I though quaterly meant "cuatrimestralmente" in spanish, which means every four months.

Verbal is killing me even in the Quantitative section

pankajks2010 wrote:In a year there are 4 quarters and every quarter has 3 months.

Thus, the annual interest rate would get divided by 4 and not 3.

Similarly, the time period (n) would become 2*4=8 and not 6.

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