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Ron deposits $400 in savings account which gives compound interest

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Ron deposits $400 in savings account which gives compound interest  [#permalink]

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New post 08 Oct 2017, 09:54
1
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

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

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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

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Ron deposits $400 in savings account which gives compound interest  [#permalink]

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New post 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.

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Re: Ron deposits $400 in savings account which gives compound interest  [#permalink]

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New post 06 Feb 2019, 08:38
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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).

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Re: Ron deposits $400 in savings account which gives compound interest   [#permalink] 06 Feb 2019, 08:38
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