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A certain investment grows at an annual interest rate of 8%, compounde
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23 Mar 2021, 05:30
23 Mar 2021, 05:30
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58% (01:46) wrong based on 62 sessions
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A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
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Re: A certain investment grows at an annual interest rate of 8%, compounde
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23 Mar 2021, 09:32
23 Mar 2021, 09:32
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GeminiHeat wrote:
A certain investment grows at an annual interest rate of 8%, compounded quarterly. Which of the following equations can be solved to find the number of years, x, that it would take for the investment to increase by a factor of 16?
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
A. 16 = 1.02^(x/4)
B. 2 = 1.02^x
C. 16 = 1.08^(4x)
D. 2 = 1.02^(x/4)
E. 1/16 = 1.02^(4x)
\(Amount = P [1 + \frac{R}{100n}]^{nT}\)
\(T\) = time in years
\(n\) = number of times, interest is calculated
As per the question:
\(16P = P [1 + \frac{8}{100(4)}]^{4x}\)
\(16 = [1 + \frac{2}{100}]^{4x}\)
\(16 = (1.02)^{4x}\)
\(2^4 = (1.02)^{4x}\)
\(2 = (1.02)^x\)
Hence, option B
General Discussion
Re: A certain investment grows at an annual interest rate of 8%, compounde
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05 Jan 2022, 19:57
05 Jan 2022, 19:57
Can someone explain how this question makes sense? Why would it matter that the interest rate is compounded quarterly when we already know the annual interest rate is 8%? Shouldn't the answer be 16=1.08^x, since x is in years? I do not think that we are allowed to assume that the 8% is convertible quarterly when it explicitly states "annual interest rate".
