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1
6 00:00

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] Show Tags 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]

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_________________ Re: Ron deposits $400 in savings account which gives compound interest [#permalink] 06 Feb 2019, 08:38 Display posts from previous: Sort by Ron deposits$400 in savings account which gives compound interest

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