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## OG Problem Solving Q 78

This topic has 3 expert replies and 4 member replies
melguy Master | Next Rank: 500 Posts
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#### OG Problem Solving Q 78

Wed Oct 12, 2011 7:46 pm
Hello All

I tried searching explanation for the below question in the forum but could not find a good answer. I would appreciate if anyone could plz help.

Leona bought a 1-year, $10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity? (A)$10,464
(B) $864 (C)$ 816
(D) $800 (E)$ 480

I am just curious to know that the Q states "8 percent compounded semiannually" so why do we need to multiply by .04% two times.

I understand the process but I am curious as to why don't we multiply by .08% two times instead of .04% since the interest rate is 8% not 4%. Be it semi annually or annually the interest rate is the same?

Thanks

### GMAT/MBA Expert

GmatMathPro GMAT Instructor
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Wed Oct 12, 2011 8:30 pm
Interest rates are almost universally quoted on an annual basis. So when they say the interest rate is 8%, that is an annual interest rate. So, if we invest $100 at 8% compounded annually, at the end of one year we would have$108. Halfway through the year we would have $104. Now, when we change it to 8% compounded semiannually, that is still an annual interest rate. We are just compounding it more frequently. The phrase "8 percent compounded semiannually" really means an 8 percent annual interest rate compounded semi-annually. They just don't include the part about it being an annual interest rate because it is understood. _________________ Pete Ackley GMAT Math Pro Free Online Tutoring Trial fcabanski Master | Next Rank: 500 Posts Joined 07 Oct 2011 Posted: 104 messages Followed by: 3 members Upvotes: 36 Wed Oct 12, 2011 9:21 pm Not sure if I'm reading this correctly, but a formula for compound interest is: A = P(1+r/n)^nt A is the principal plus accumulated interest. P is the principal. A-P then answers this question - the amount of interest accumulated. r is the annual interest rate. n is the number of compound periods in a year. t is the number of years. This one is simple. So you can solve it without knowing the compound interest formula as long as you know: - The principal applied in each compound period is the annual rate divided by the number of compound periods. - Compound interest means the interest in each period applies to the total of principal and interest accumulated in all previous periods. The balance in each period is the principal plus ...the principal times the annual rate divided by the number of compound periods. 1st period. 10,000+ 10,000*.08/2 = 10,400 2nd period. 10,400 + 10,400*.08/2 = 10816. Interest accumulated = 10,816 - 10,000 = 816 Last edited by fcabanski on Wed Oct 12, 2011 9:29 pm; edited 1 time in total shankar.ashwin Legendary Member Joined 02 Jan 2010 Posted: 966 messages Followed by: 21 members Upvotes: 230 Wed Oct 12, 2011 9:26 pm Interest rates for semiannually is similar to how you would normally calculate interests. 2 things to remember: Interest rates would be R%/n (R% - rate of interest) (n - number of times interest is calculated) Here, you have 8% compounded semiannually, so r - 8% and n - 2 (1 year - semiannually) Hence rate for calculation would be R%/n - 8/2 = 4% and number of terms would be 2. Amt = P[1 + (r/100)]^n = 10000[(1 + 0.04]^2 = 10816 Interest would be 10816 - 10000 = 816 ### GMAT/MBA Expert GMATGuruNY GMAT Instructor Joined 25 May 2010 Posted: 14164 messages Followed by: 1818 members Upvotes: 13060 GMAT Score: 790 Thu Oct 13, 2011 2:59 am melguy wrote: Hello All I tried searching explanation for the below question in the forum but could not find a good answer. I would appreciate if anyone could plz help. Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 I am just curious to know that the Q states "8 percent compounded semiannually" so why do we need to multiply by .04% two times. I understand the process but I am curious as to why don't we multiply by .08% two times instead of .04% since the interest rate is 8% not 4%. Be it semi annually or annually the interest rate is the same? Thanks When the time period is brief, the compounded interest will be just a bit more than the simple interest. Simple interest = .08(10,000) = 800. The correct answer must be just a bit more than 800. The correct answer is C. _________________ Mitch Hunt GMAT Private Tutor GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. fcabanski Master | Next Rank: 500 Posts Joined 07 Oct 2011 Posted: 104 messages Followed by: 3 members Upvotes: 36 Thu Oct 13, 2011 8:43 am That's a good way to look at it and to solve it quickly. ### GMAT/MBA Expert Jeff@TargetTestPrep GMAT Instructor Joined 09 Apr 2015 Posted: 992 messages Followed by: 13 members Upvotes: 39 Wed May 20, 2015 3:06 pm melguy wrote: Hello All I tried searching explanation for the below question in the forum but could not find a good answer. I would appreciate if anyone could plz help. Leona bought a 1-year,$10,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?

(A) $10,464 (B)$ 864
(C) $816 (D)$ 800
(E) $480 I am just curious to know that the Q states "8 percent compounded semiannually" so why do we need to multiply by .04% two times. I understand the process but I am curious as to why don't we multiply by .08% two times instead of .04% since the interest rate is 8% not 4%. Be it semi annually or annually the interest rate is the same? Thanks We could have also looked at this problem a bit more conceptually. We know that when an investment has a rate of 8% ANNUAL interest and it compounds SEMI-ANNUALLY (twice a year), the investment earns 4% interest every SIX MONTHS. So in this case we know: Interest earned for the first six months = 0.04 x$10,000 = $400 Her investment is now worth ($400 + $10,000) =$10,400

Interest earned for the next six months = 0.04 x $10,400 =$416

Thus, the total interest earned = $400 +$416 = \$816

_________________
Jeffrey Miller Head of GMAT Instruction

nikhilgmat31 Legendary Member
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Fri May 22, 2015 4:40 am
In simple terms-

Principal+ Interest for in first Term of 6 months becomes principal for next six moths.

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