GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Oct 2019, 15:47

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

### Show Tags

03 Jul 2017, 18:01
1
2
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:52) correct 8% (01:05) wrong based on 113 sessions

### HideShow timer Statistics

If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars? A. $$10,000(1+ \frac{0.08}{2})^{10}$$ B. $$10,000(1+0.08)^5$$ C. $$10,000(1+0.08)$$ D. $$10,000(1-0.08)^2$$ E. $$10,000*1.08$$ _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Math Expert
Joined: 02 Aug 2009
Posts: 7959
Re: If $10,000 is invested at 8 percent annual interest, compounded semian [#permalink] ### Show Tags 03 Jul 2017, 19:56 1 MathRevolution wrote: If$10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars?

A. $$10,000(1+ \frac{0.08}{2})^{10}$$
B. $$10,000(1+0.08)^5$$
C. $$10,000(1+0.08)$$
D. $$10,000(1-0.08)^2$$
E. $$10,000*1.08$$

Whenever an amount is compounded semi-annually, the interest rate becomes half and TIME becomes two times..
So
1) Rate becomes 0.08/2
2) Time becomes 5*2=10

A is correct
_________________
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 3341
Location: India
GPA: 3.12
Re: If $10,000 is invested at 8 percent annual interest, compounded semian [#permalink] ### Show Tags 04 Jul 2017, 00:51 Compound interest = $$Amount * (1 + \frac{ROI}{100})^n$$ where ROI is the rate of interest n is the amount of years the amount is invested When an amount is invested and interest is calculated semi-annually, the rate of interest is halved and the number of years doubles. The formula for compound interest is : Compound interest = $$Amount * (1 + \frac{ROI}{200})^{2n}$$ Coming to the problem in hand, Amount : 10000$
Interest(annual)-ROI : 8% = $$\frac{8}{100} = 0.08$$
Number of years-n : 5

Substituting these values, Interest = $$10,000(1+ \frac{0.08}{2})^{10}$$ (Option A)

_________________
You've got what it takes, but it will take everything you've got
Senior SC Moderator
Joined: 22 May 2016
Posts: 3544
If $10,000 is invested at 8 percent annual interest, compounded semian [#permalink] ### Show Tags 04 Jul 2017, 04:15 MathRevolution wrote: If$10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars?

A. $$10,000(1+ \frac{0.08}{2})^{10}$$
B. $$10,000(1+0.08)^5$$
C. $$10,000(1+0.08)$$
D. $$10,000(1-0.08)^2$$
E. $$10,000*1.08$$

The formula for compound interest can be written in a few ways. IMO, the version that matches the answer choices most closely is

A = P $$(1+ \frac{r}{n})^{nt}$$

A= amount of money accumulated over t years, including interest (what the question asks for)
P = initial amount invested
r = annual rate of interest in decimal form
n = the number of times the interest is compounded annually
t = number of years the amount is deposited (or borrowed) for
nt = # of times per year interest is compounded times # of years

P = $10,000 r = .08 n = 2 (semi-annually = twice per year) t = 5 (years) $$\frac{r}{n}$$ = $$\frac{.08}{2}$$ nt = 2*5 = 10 Using figures above, the equation becomes A = $$10,000(1+ \frac{0.08}{2})^{10}$$ Answer A _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Choose life. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If$10,000 is invested at 8 percent annual interest, compounded semian  [#permalink]

### Show Tags

05 Jul 2017, 01:03
==> if it is invested at 8 percent annual interest and is compounded semiannually, From
10,000(1+8%$$(\frac{1}{2}))^{2*5}= 10,000(1+)^{10}$$ the answer is A

_________________
MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior PS Moderator Joined: 26 Feb 2016 Posts: 3341 Location: India GPA: 3.12 Re: If$10,000 is invested at 8 percent annual interest, compounded semian  [#permalink]

### Show Tags

05 Jul 2017, 01:30
MathRevolution wrote:
==> if it is invested at 8 percent annual interest and is compounded semiannually, From
10,000(1+8%$$(\frac{1}{2}))^{2*5}= 10,000(1+)^{10}$$ the answer is A

_________________
You've got what it takes, but it will take everything you've got
Intern
Joined: 02 May 2018
Posts: 12
GMAT 1: 620 Q46 V29
Re: If $10,000 is invested at 8 percent annual interest, compounded semian [#permalink] ### Show Tags 10 Sep 2018, 07:37 1 generis wrote: MathRevolution wrote: If$10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars?

A. $$10,000(1+ \frac{0.08}{2})^{10}$$
B. $$10,000(1+0.08)^5$$
C. $$10,000(1+0.08)$$
D. $$10,000(1-0.08)^2$$
E. $$10,000*1.08$$

The formula for compound interest can be written in a few ways. IMO, the version that matches the answer choices most closely is

A = P $$(1+ \frac{r}{n})^{nt}$$

A= amount of money accumulated over t years, including interest (what the question asks for)
P = initial amount invested
r = annual rate of interest in decimal form
n = the number of times the interest is compounded annually
t = number of years the amount is deposited (or borrowed) for
nt = # of times per year interest is compounded times # of years

P = $10,000 r = .08 n = 2 (semi-annually = twice per year) t = 5 (years) $$\frac{r}{n}$$ = $$\frac{.08}{2}$$ nt = 2*5 = 10 Using figures above, the equation becomes A = $$10,000(1+ \frac{0.08}{2})^{10}$$ Answer A A slightly modified formula. Just for ease of use. A = P $$(1+ \frac{r}{100n})^{nt}$$ Re: If$10,000 is invested at 8 percent annual interest, compounded semian   [#permalink] 10 Sep 2018, 07:37
Display posts from previous: Sort by