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25 Mar 2026, 22:24
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A
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Difficulty:
65%
(hard)
Question Stats:
66% (03:00) correct
34%
(02:14)
wrong
based on 112
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Alvaro invests $1,000 at 6% interest compounded semiannually for 8 years. He then invests the accumulated amount at 8% interest compounded quarterly for 5 years.
\(x = (1.03)^8 \quad \text{and} \quad y = (1.02)^{12}\)
Which of the following is equivalent to the final balance in dollars?
\(\text{A.}\quad \frac{1000 (xy)^2}{\sqrt[3]{y}}\)
\(\text{B.}\quad 1000 (xy)^2\)
\(\text{C.}\quad 1000 x^2 y\)
\(\text{D.}\quad \frac{1000 (xy)^2}{\sqrt{y}}\)
\(\text{E.}\quad \frac{1000 x y^2}{\sqrt[3]{y}}\)
\(x = (1.03)^8 \quad \text{and} \quad y = (1.02)^{12}\)
Which of the following is equivalent to the final balance in dollars?
\(\text{A.}\quad \frac{1000 (xy)^2}{\sqrt[3]{y}}\)
\(\text{B.}\quad 1000 (xy)^2\)
\(\text{C.}\quad 1000 x^2 y\)
\(\text{D.}\quad \frac{1000 (xy)^2}{\sqrt{y}}\)
\(\text{E.}\quad \frac{1000 x y^2}{\sqrt[3]{y}}\)
04 Apr 2026, 14:07
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kevincan
Alvaro accumulated amt at the end of \(8\) yrs :
Using C.I. Formula
\(= 1000 ( 1 + \frac{6}{100 * 2})^{8*2}\)
\(= 1000 ( 1 + \frac{3}{100})^{16}\)
\(= 1000 (1.03)^{16}\)
Accumulated amt becomes the principal for the next \(5\) years:
\(= 1000 (1.03)^{16} ( 1 + \frac{8}{100 * 4})^{5*4}\)
\(= 1000 (1.03)^{16} ( 1+ \frac{2}{100})^{20}\)
\(= 1000 (1.03)^{16} (1.02)^{20}\)
\(= 1000 (x)^2 y^{( \frac{5}{3})}\)
\(= \frac{1000*{(xy)}^{2}}{y^{(\frac{1}{3})}\)
Ans A
Hope it helped.
