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03 Jul 2017, 18:01
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
94% (00:49) correct
6%
(01:07)
wrong
based on 210
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If $10,000 is invested at 8 percent annual interest, compounded semiannually, what is the balance after 5 year, in terms of dollars?
A. \(10,000(1+ \frac{0.08}{2})^{10}\)
B. \(10,000(1+0.08)^5\)
C. \(10,000(1+0.08)\)
D. \(10,000(1-0.08)^2\)
E. \(10,000*1.08\)
A. \(10,000(1+ \frac{0.08}{2})^{10}\)
B. \(10,000(1+0.08)^5\)
C. \(10,000(1+0.08)\)
D. \(10,000(1-0.08)^2\)
E. \(10,000*1.08\)
03 Jul 2017, 19:56
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MathRevolution
Whenever an amount is compounded semi-annually, the interest rate becomes half and TIME becomes two times..
So
1) Rate becomes 0.08/2
2) Time becomes 5*2=10
A is correct
04 Jul 2017, 00:51
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Compound interest = \(Amount * (1 + \frac{ROI}{100})^n\)
where
ROI is the rate of interest
n is the amount of years the amount is invested
When an amount is invested and interest is calculated semi-annually,
the rate of interest is halved and the number of years doubles.
The formula for compound interest is :
Compound interest = \(Amount * (1 + \frac{ROI}{200})^{2n}\)
Coming to the problem in hand,
Amount : 10000$
Interest(annual)-ROI : 8% = \(\frac{8}{100} = 0.08\)
Number of years-n : 5
Substituting these values, Interest = \(10,000(1+ \frac{0.08}{2})^{10}\) (Option A)
where
ROI is the rate of interest
n is the amount of years the amount is invested
When an amount is invested and interest is calculated semi-annually,
the rate of interest is halved and the number of years doubles.
The formula for compound interest is :
Compound interest = \(Amount * (1 + \frac{ROI}{200})^{2n}\)
Coming to the problem in hand,
Amount : 10000$
Interest(annual)-ROI : 8% = \(\frac{8}{100} = 0.08\)
Number of years-n : 5
Substituting these values, Interest = \(10,000(1+ \frac{0.08}{2})^{10}\) (Option A)
