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02 Dec 2019, 01:17
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D
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Difficulty:
95%
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Question Stats:
39% (03:05) correct
61%
(02:48)
wrong
based on 62
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Jennifer invests $2,000 at an annual interest rate of r% compounded quarterly for 9 years. At the end of 9 years her account is worth $16,000. What is the value of r?
A. \(400(2\cdot4^{\frac{1}{9}}-1)\)
B. \(25(2^{\frac{25}{36}}-1)\)
C. \(100\cdot8^{\frac{1}{9}}-1\)
D. \(25\cdot2^{\frac{49}{12}}-400\)
E. \(400\cdot8^{\frac{1}{36}}-200\)
A. \(400(2\cdot4^{\frac{1}{9}}-1)\)
B. \(25(2^{\frac{25}{36}}-1)\)
C. \(100\cdot8^{\frac{1}{9}}-1\)
D. \(25\cdot2^{\frac{49}{12}}-400\)
E. \(400\cdot8^{\frac{1}{36}}-200\)
04 Dec 2019, 08:47
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Amount=16000; Principal=2000;
Year = 9(total term=9*4=36)
Formula for compound intrest:
A=P\((1+\frac{r}{100*n})^nt\)
Where, A is Amount; P is Principal; r is rate; n is number of times; t is year
Substituting the values
16000=2000\((1+\frac{r}{100*4})^36\)
Solving above we get the value as :
\((8)^(\frac{1}{36})\)=\((\frac{400+r}{400})\)
on solving we get r value as \(400.(8)^(\frac{1}{36})-400\)
Year = 9(total term=9*4=36)
Formula for compound intrest:
A=P\((1+\frac{r}{100*n})^nt\)
Where, A is Amount; P is Principal; r is rate; n is number of times; t is year
Substituting the values
16000=2000\((1+\frac{r}{100*4})^36\)
Solving above we get the value as :
\((8)^(\frac{1}{36})\)=\((\frac{400+r}{400})\)
on solving we get r value as \(400.(8)^(\frac{1}{36})-400\)
04 Dec 2019, 12:31
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Bunuel looks like D and E have the exact same value?
\(400 * 8^{1/36} = 25 * 2^4 * (2^3)^{1/36} = 25 * 2^4 * 2^{1/12} = 25 * 2^{49/12} \)
\(400 * 8^{1/36} = 25 * 2^4 * (2^3)^{1/36} = 25 * 2^4 * 2^{1/12} = 25 * 2^{49/12} \)
Bunuel
Jennifer invests $2,000 at an annual interest rate of r% compounded quarterly for 9 years. At the end of 9 years her account is worth $16,000. What is the value of r?
A. \(400(2\cdot4^{\frac{1}{9}}-1)\)
B. \(25(2^{\frac{25}{36}}-1)\)
C. \(100\cdot8^{\frac{1}{9}}-1\)
D. \(25\cdot2^{\frac{49}{12}}-400\)
E. \(400\cdot8^{\frac{1}{36}}-400\)
A. \(400(2\cdot4^{\frac{1}{9}}-1)\)
B. \(25(2^{\frac{25}{36}}-1)\)
C. \(100\cdot8^{\frac{1}{9}}-1\)
D. \(25\cdot2^{\frac{49}{12}}-400\)
E. \(400\cdot8^{\frac{1}{36}}-400\)
