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E
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Difficulty:
35%
(medium)
Question Stats:
81% (02:15) correct
19%
(02:30)
wrong
based on 521
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What amount, in dollars, invested for one year at a simple annual interest of 2 percent would earn the same amount of interest as $10,000 invested for one year at an annual interest rate of 4 percent compounded semiannually?
A. $20,000
B. $20,050
C. $20,100
D. $20,150
E. $20,200
A. $20,000
B. $20,050
C. $20,100
D. $20,150
E. $20,200
19 Dec 2023, 00:02
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pablovaldesvega
What amount, in dollars, invested for one year at a simple annual interest of 2 percent would earn the same amount of interest as $10,000 invested for one year at an annual interest rate of 4 percent compounded semiannually?
A. $20,000
B. $20,050
C. $20,100
D. $20,150
E. $20,200
A. $20,000
B. $20,050
C. $20,100
D. $20,150
E. $20,200
An annual rate of 4 percent compounded semiannually is effectively 2 percent every six months, applied twice within the year (at the end of the 6th and 12th months). Therefore, the final balance after one year for $10,000 invested at an annual interest rate of 4 percent compounded semiannually will be calculated as follows:
- \($10,000*(1+\frac{0.04}{2})^{1*2}=\)
\(=$10,000*(1.02)^{2}=\)
\(=$10,000*\frac{102^2}{100^2}=\)
\(=$102^2=\)
\(=$(100+2)^2=\)
\( = $100^2+4*100+4\)
\(= $10,404\).
Thus, $10,000 invested for one year at an annual interest rate of 4 percent compounded semiannually would earn $404.
An amount invested for one year at a simple annual interest of 2 percent to earn $404 is $404/0.02 = $404/(1/50) = $404*50 = $20,200.
Answer: E.
28 Jan 2024, 03:09
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