Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
07 Dec 2012, 03:29
Question Stats:
74% (01:07) correct 26% (01:22) wrong based on 2184 sessions
HideShow timer Statistics
Leona bought a 1year, $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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 49273

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
07 Dec 2012, 03:35
Walkabout wrote: Leona bought a 1year, $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 Approach #1:8 percent compounded semiannually > 4% in 6 moths. For the first 6 moths interest was 4% of $10,000, so $400; For the next 6 moths interest was 4% of $10,000, plus 4% earned on previous interest of $400, so $400+$16=$416; Total interest for 1 year was $400+$416=$816. Answer: C. Approach #2:If the interest were compounded annually instead of semiannually then in a year the interest would be 8% of $10,000, so $800. Now, since the interest is compounded semiannually then there would be interest earned on interest (very small amount) thus the actual interest should be a little bit more than $800, only answer choice C fits. Answer: C. Similar questions to practice: johndeposited10000toopenanewsavingsaccountthat135825.htmlonthefirstoftheyearjamesinvestedxdollarsat128825.htmlmarcusdeposited8000toopenanewsavingsaccountthat128395.htmljoleneenteredan18monthinvestmentcontractthat127308.htmlalexdepositedxdollarsintoanewaccount126459.htmlmichelledepositedacertainsumofmoneyinasavings138273.htmlTheory: mathnumbertheorypercents91708.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Intern
Joined: 09 Apr 2013
Posts: 41
Location: United States (DC)
Concentration: Strategy, Social Entrepreneurship
GPA: 3.55
WE: General Management (NonProfit and Government)

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
10 Jun 2013, 05:43
The equation for compound interest is: \(P_t = P_0(1+\frac{i}{n})^{nt}\) \(P_t\) is the Principle at time t \(P_0\) is the Principle at time 0 \(i\) is the Interest Rate \(n\) is the Number of compounding periods \(t\) is the Number of years the investment earns interest
Plug in the numbers: \(P_t = 10,000(1+\frac{.08}{2})^{2*1}\)
\(P_t = 10,000(1+\frac{8}{200})^{2}\)
\(P_t = 10,000(\frac{200}{200}+\frac{8}{200})^{2}\)
\(P_t = 10,000(\frac{208}{200})^{2}\)
\(P_t = 10,000(\frac{104}{100})^{2}\)
\(P_t = 10,000(\frac{10,816}{10,000})\)
\(P_t = 10,816\)
\(P_t  P_0= 10,816  10,000 = 816\)
Answer is C
Definitely a more difficult solution, but I know some people really like formulas.




Manager
Joined: 11 Aug 2012
Posts: 122

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
25 Dec 2012, 16:52
Bunuel, are the interest questions in the real GMAT as easy as this one?



Math Expert
Joined: 02 Sep 2009
Posts: 49273

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
10 Jun 2013, 05:09



Intern
Joined: 10 Jan 2012
Posts: 22
Concentration: Strategy, Finance
GMAT Date: 10172013
WE: Consulting (Computer Software)

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
26 Jun 2013, 00:32
This problem can be solved using formula. However, the calculation in formula is difficult = 10,000(208/200)^2. The main motive of GMAT behind Compound interest problem is to consume your time so that you waste your precious time in difficult calculations. We have to avoid that trap and use simple and fast calculations. By definition Compound interest = S.I. + Interest on Interest So here C.I. = 4% on 10,000 (6months) + 4% on 10,000(6months) + 4% on interest (last 6 months interest) = 400 + 400 + 4*400/100 = 400 + 400 + 16 = 816
_________________
Thanks & Regards Yodee
‘A good plan violently executed now is better than a perfect plan executed next week.’  General Georg S. Patton



Intern
Joined: 19 Jan 2014
Posts: 26

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
25 May 2014, 16:47
Walkabout wrote: Leona bought a 1year, $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 did it this way. I find it to be easy way for compound interest questions so maybe it will help someone. annual interest 8%. semiannual = 4% (8/2) how many times 4%? 2 times 10 000x104/100x104/100=104x104=10 816 10 81610 000=816



Intern
Affiliations: ScoreBoost
Joined: 07 Sep 2012
Posts: 14
Location: India

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
27 May 2014, 03:18
The amount increases in two steps : 4% in the first 6 months and again 4% in the second 6 months. Such % change in two steps is knows as successive % change. In case of successive % change, we can use the below formula to calculate the Net % change : \(Net % change =\) \(A + B + \frac{AB}{100}\) If there is % increase , we take the value as positive and for % decrease, we take that as negative. In the final answer, positive number shows % increase and negative number shows % decrease. Using the above formula , we get : net change = \(4 + 4 + \frac{4*4}{100}\) \(= 8 + .16 = 8.16 %\). \(8.16 % of 10,000\) is 816. Hence the answer is 816. This formula is applicable only in case of % change in two steps. In case % change takes place in 3 steps, we have to apply the formula for the first two first and then to the result and the third one.
_________________
Quant Instructor ScoreBoost Bangalore, India



Intern
Joined: 11 Nov 2014
Posts: 12
GMAT Date: 01152015
GPA: 3.4

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
15 Nov 2014, 05:35
I used the simple interest formula. which should give you 800 and slightly above that should give you the compound interest answer. therefore C
i think this is the best way to save time.



Intern
Joined: 09 Dec 2014
Posts: 6
Location: United States

Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
14 Apr 2015, 08:43
Is this approach correct?
Interest= (P*R*T)/100
For first 6 months, I = (10000*8*0.5)/100=400 Amount = P + I = 10400
For second 6 months, previous amount becomes the principal I = (10400*8*0.5)/100= 416
So total interest = 400+416=816



Retired Moderator
Joined: 23 Sep 2015
Posts: 385
Location: France
GMAT 1: 690 Q47 V38 GMAT 2: 700 Q48 V38
WE: Real Estate (Mutual Funds and Brokerage)

Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
23 Nov 2015, 14:34
the interest is (1 + 0.08/2)² or 1,04*1,04 = 1,0816 or 8,16% If compounded annualy : (1 + 0,08) or 8% Compounded quaterly : (1 + 0,08/4)^4 or, 1,02^4 = 8,24% The shorter the compound period, the higher the interest payment.
_________________
New Application Tracker : update your school profiles instantly!



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 3517
Location: United States (CA)

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
07 Jun 2016, 10:55
Walkabout wrote: Leona bought a 1year, $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 We use the compound interest equation: Future Value = (Present Value)(1 + r/n)^nt where r is the annual interest rate, n is the number of compounding periods per year and t is the amount of time (in years) until maturity. So we know: Present Value = 10,000 r = 8% = 0.08 n = 2 t = 1 So we have: FV = 10,000(1+0.08/2)^(2)(1) FV = 10,000(1+0.04)^2 FV = 10,000(1.04)(1.04) FV = 10,000(1.0816) = $10,816 Thus, the amount of interest earned is $10,816 – $10,000 = $816. 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 SEMIANNUALLY (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 Answer is C
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 21 Sep 2015
Posts: 80
Location: India
GMAT 1: 730 Q48 V42 GMAT 2: 750 Q50 V41

Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
12 Jun 2016, 05:44
A = 10000 * ( 1 +8 / 200) ^2 = 10000* (1.04 )^2 =104 * 10 Therefore units place of answer should have 6 Ans: 816 ScottTargetTestPrep why would anyone want to multiply 1.04 * 1.04
_________________
Appreciate any KUDOS given !



Current Student
Joined: 18 Oct 2014
Posts: 874
Location: United States
GPA: 3.98

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
12 Jun 2016, 09:00
Walkabout wrote: Leona bought a 1year, $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 Compound interest= P (1+r/100n)^n 10,000 (1+8/200)^2 10,000 * 104/100 *104/100 Units digit will be 6. Only option C has units digit of 6
_________________
I welcome critical analysis of my post!! That will help me reach 700+



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4020
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
27 Jun 2017, 08:36
Walkabout wrote: Leona bought a 1year, $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 \(A = 10000 ( 1 + \frac{8}{200})^2\) Or, \(A = 10000*1.04^2\) Or, \(A = 10816\) So, Interest paid on this certificate at maturity is $ 816, answer must be (C)
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Retired Moderator
Joined: 19 Mar 2014
Posts: 962
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
27 Jun 2017, 12:57
Leona bought a 1year, $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?1. Premium for first 6 months: \(10,000 * \frac{8}{100}\) = \($ 800\) As the interest is getting compounded semiannually, new principal will be = \($ 10,000 + $ 800\) = \($ 10,800\) 2. Premium for next 6 months: \(10,800 * \frac{80}{100}\)= \($816\) Hence, Total Interest Paid = \($ 816\) Hence, the Answer is C
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."
Best AWA Template: https://gmatclub.com/forum/howtoget60awamyguide64327.html#p470475



Director
Joined: 02 Sep 2016
Posts: 721

Re: Leona bought a 1year, $10,000 certificate of deposit that
[#permalink]
Show Tags
10 Sep 2017, 02:38
Compound interest formula is the best way to solve this problem. But we can also use the simple interest formula: Amount*Rate*Time/100 = 10000*8*1/100 =800 The answer would be slightly more than 800 i.e. 816.
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.




Re: Leona bought a 1year, $10,000 certificate of deposit that &nbs
[#permalink]
10 Sep 2017, 02:38






