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

 It is currently 14 Oct 2019, 18:24

### 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

08 Oct 2017, 09:54
1
6
00:00

Difficulty:

45% (medium)

Question Stats:

63% (02:03) correct 37% (02:22) wrong based on 49 sessions

### HideShow timer Statistics

Ron deposits $400 in savings account which gives compound interest semi-annually at the rate of 8% p.a. Approximately, how much interest does he receive in 2 years? (A)$60

(B) $64 (C)$68

(D) $72 (E)$76

_________________
Senior SC Moderator
Joined: 22 May 2016
Posts: 3537
Ron deposits $400 in savings account which gives compound interest [#permalink] ### Show Tags 08 Oct 2017, 19:52 2 HKD1710 wrote: Ron deposits$400 in savings account which gives compound interest semi-annually at the rate of 8% p.a. Approximately, how much interest does he receive in 2 years?

(A) $60 (B)$64

(C) $68 (D)$72

(E) $76 Ron's money earns 1.04 percent interest every six months over two years for a total of four payments. Total amount earned with compound interest** is given by $$A = P(1 + \frac{r}{n})^{nt}$$, thus $$400(1.04)^4$$ The problem: the arithmetic and these answers. 1.04$$^{x}$$ behaves much differently than .04$$^{x}$$ does. There are more numbers and more decimal places to multiply. And these answer choices are wickedly close. I decided that a yearly compounding rate of 1.08 * 1.08 would have to be close enough. 1.08 * 1.08 = 1.1664 1.1664 *$400 = $466.56 I had rounded down: fewer compounding periods always produces less interest earned. The actual figure would be slightly more than$466.56.

I was annoyed enough by then that "pretty close" was good enough.*

Interest earned (subtract principal):
($466.56 -$400) = $66.56 = approximately$68
($66.56 is closer to$68 than to $64) Answer C I don't usually announce time taken. I think it matters here: 56 seconds. It's doable. *After, I multiplied on a calculator to see the actual figures: 1.04$$^4$$ = 1.16985856, *$400 = $467.943424 From above, by hand: 1.08 * 1.08 = 1.1664, *$400 = $466.56 The first answer is exact and decisively points you to C. The second isn't as decisive, but if you remember that you have rounded down using 1.08, Answer C is the right choice. ** r is the decimal interest rate n is the number of periods t is time in years P is principal Total amount Divide .08 by 2 = .04 Add .04 to 1 = 1.04 = rate of interest payment every 6 months. There are 2 pay periods per year, times 2 years = 4 payments. _________________ SC Butler has resumed! Get two SC questions to practice, whose links you can find by date, here. Choose life. Non-Human User Joined: 09 Sep 2013 Posts: 13142 Re: Ron deposits$400 in savings account which gives compound interest  [#permalink]

### Show Tags

06 Feb 2019, 08:38
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________