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Carcass invested $2,000 at a ceratin rate of interest compounded semi-
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02 Sep 2021, 03:59
02 Sep 2021, 03:59
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Question Stats:
35% (01:38) correct
64% (02:45) wrong based on 28 sessions
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Carcass invested $2,000 at a certain rate of interest compounded semi-annually. At the end of 5 years, the total value of the amount will be $6,000.
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Quantity A |
Quantity B |
Number of years in which total amount will become $54,000 |
15 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Carcass invested $2,000 at a ceratin rate of interest compounded semi-
[#permalink]
02 Sep 2021, 18:02
02 Sep 2021, 18:02
4
Start by writing out the equation:
\(2000\)\((1+\)\(\frac{i}{200}\)\()^{10}\)\(=6000\)
Now divide both sides by 2000:
\((1+\)\(\frac{i}{200}\)\()^{10}\)\(=3\)
We want to manipulate the equation in order to get the exponent to become 30, which represents 15 years of investment semi-annually.
To do this, cube both sides of the equation:
\([\)\((1+\)\(\frac{i}{200}\)\()^{10}\)\(]^3\)\(=(3)^3\)
\((1+\)\(\frac{i}{200}\)\()^{30}\)\(=27\)
Now multiply both sides by 2000 again:
\(2000\)\((1+\)\(\frac{i}{200}\)\()^{30}\)\(=54000\)
We have that, after 15 years, the $2000 investment compounded semiannually will be $54000.
Therefore, the answer is C
\(2000\)\((1+\)\(\frac{i}{200}\)\()^{10}\)\(=6000\)
Now divide both sides by 2000:
\((1+\)\(\frac{i}{200}\)\()^{10}\)\(=3\)
We want to manipulate the equation in order to get the exponent to become 30, which represents 15 years of investment semi-annually.
To do this, cube both sides of the equation:
\([\)\((1+\)\(\frac{i}{200}\)\()^{10}\)\(]^3\)\(=(3)^3\)
\((1+\)\(\frac{i}{200}\)\()^{30}\)\(=27\)
Now multiply both sides by 2000 again:
\(2000\)\((1+\)\(\frac{i}{200}\)\()^{30}\)\(=54000\)
We have that, after 15 years, the $2000 investment compounded semiannually will be $54000.
Therefore, the answer is C
Re: Carcass invested $2,000 at a ceratin rate of interest compounded semi-
[#permalink]
03 Sep 2021, 00:02
03 Sep 2021, 00:02
2
2
Expert Reply
I do not have so much money 
