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08 Oct 2017, 09:54
4
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:22) correct 33% (01:33) wrong based on 40 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] ### Show Tags 08 Oct 2017, 19:52 1 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, so 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 was going to have to be close enough. 1.08 * 1.08 = 1.1664 1.1664 *$400 = $466.56 I had rounded down. The actual figure would be slightly more than that. And I was annoyed enough by then that "pretty close" was good enough.* Interest earned:$466.56 - 400 = $66.56 = approximately$68

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, and two years = 4 payments. _________________ In the depths of winter, I finally learned that within me there lay an invincible summer. -- Albert Camus, "Return to Tipasa" Ron deposits$400 in savings account which gives compound interest &nbs [#permalink] 08 Oct 2017, 19:52
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