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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