Roxie invested $2000 in an account that yielded a fixed rate of annual return compounded annually throughout the duration of investment. If she earned a total interest of $4000 in 6 years, after how many years of investment did she earn a total interest of $52000?
A.18
B.28
C.30
D.56
E. Cannot be determined
[spoiler]OA=A[/spoiler]
Source: eGMAT
Roxie invested $2000 in an account that yielded a fixed rate of annual return compounded annually throughout the duratio
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Given that: p = 2000
Total interest in 6 years = 4000
Money in the account after 6 years = 2000 + 4000 = 6000
Hence, money in the account is going to be; principal * 3 every 6 years
Target question => After how many years of investment did she earn a total interest of $52000?
Let the number of years to earn $52000 = x
Total money in the account after x years =>
$52000 + 2000 = 54000
Knowing that investment triples every 6 years
$$For\ the\ first\ 6000:\ \frac{6000}{2000}=3=3^1$$
$$Number\ of\ years\ =\ 1\cdot6=6\ years$$
$$For\ the\ new\ 54000\ =\ \frac{54000}{2000}=27=3^3$$
$$Number\ of\ years\ =3\cdot6=18\ years$$
$$Answer\ =\ A$$
Total interest in 6 years = 4000
Money in the account after 6 years = 2000 + 4000 = 6000
Hence, money in the account is going to be; principal * 3 every 6 years
Target question => After how many years of investment did she earn a total interest of $52000?
Let the number of years to earn $52000 = x
Total money in the account after x years =>
$52000 + 2000 = 54000
Knowing that investment triples every 6 years
$$For\ the\ first\ 6000:\ \frac{6000}{2000}=3=3^1$$
$$Number\ of\ years\ =\ 1\cdot6=6\ years$$
$$For\ the\ new\ 54000\ =\ \frac{54000}{2000}=27=3^3$$
$$Number\ of\ years\ =3\cdot6=18\ years$$
$$Answer\ =\ A$$
\(2000(1+R/100)^6=6000\)M7MBA wrote: ↑Wed Jun 24, 2020 6:24 amRoxie invested $2000 in an account that yielded a fixed rate of annual return compounded annually throughout the duration of investment. If she earned a total interest of $4000 in 6 years, after how many years of investment did she earn a total interest of $52000?
A.18
B.28
C.30
D.56
E. Cannot be determined
[spoiler]OA=A[/spoiler]
Source: eGMAT
\((1+R/100)^6 = 3\)
\((1+R/100) =3^{1/6}\) (don't solve further)
To find \(n\)
\(2000 (1+R/100)^n = 54000\)
\(3^{n/6}=27\)
\(3^{n/6}=3^3\)
\(n/6=3\)
\(n=18\)
Therefore, A
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Solution:M7MBA wrote: ↑Wed Jun 24, 2020 6:24 amRoxie invested $2000 in an account that yielded a fixed rate of annual return compounded annually throughout the duration of investment. If she earned a total interest of $4000 in 6 years, after how many years of investment did she earn a total interest of $52000?
A.18
B.28
C.30
D.56
E. Cannot be determined
[spoiler]OA=A[/spoiler]
We can see that in 6 years, the amount of money principal plus interest  in the account will be 2,000 + 4,000 = $6,000. This means the amount of money in the account triples every 6 years. Therefore, in 12 years, the amount of money in the account will be 6,000 x 3 = $18,000, and in 18 years, the amount of money in the account will be 18,000 x 3 = $54,000, which is $2,000 in principal and $52,000 in interest.
Answer: A
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