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12 Oct 2021, 09:00
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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:
65%
(hard)
Question Stats:
58% (02:30) correct
42%
(02:43)
wrong
based on 95
sessions
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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
A. 18
B. 28
C. 30
D. 56
E. Cannot be determined
12 Oct 2021, 11:01
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Correct Option A
(The amount of money) - (principal plus interest) - (in the account)
= 2,000 + 4,000 = $6,000.
Account triples every 6 years.
12 years = 6,000 x 3 = $18,00
18 years = 18,000 x 3 = $54,000
Principal = $2000
Interest = $52000
Posted from my mobile device
(The amount of money) - (principal plus interest) - (in the account)
= 2,000 + 4,000 = $6,000.
Account triples every 6 years.
12 years = 6,000 x 3 = $18,00
18 years = 18,000 x 3 = $54,000
Principal = $2000
Interest = $52000
Posted from my mobile device
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12 Oct 2021, 11:56
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We have been given that at the end of 6 years, after initial investment of $2000, total interest earned is Rs. 4000. Thus, money outstanding at the end of 6th year = 2000 + 4000 = 6000. Interest is compounded annually.
Thus, by using formula -
A = P x (1+r)^n,
we know that
6000 = 2000 x (1+r)^6
i.e. 3 = (1+r)^6
Let's call term (1+r) = a
Thus, we can rewrite the above equation as
3 = a^6
Thus, a = 3 ^ (1/6) ......... (Let's call it as Result I)
Now, question is by which year end, Roxie will earn total interest of 52,000 i.e. when will total outstanding be 2000 + 52000 = 54000?
By using formula, we can write -
54000 = 2000 x (1+r)^n
i.e. 27 = (1+r)^n
now, by substituting 'a' for (1+r), we rewrite above equation as
27 = a^n
i.e. 3^3 = a^n
Thus, a = (3) ^ (3/n) (Let's call it as Result II)
By comparing result I and II above, we know that
3 ^ (1/6) = (3) ^ (3/n)
i.e. 1/6 = 3/n
thus, n = 3 x 6 = 18
Hence, IMO - Option A is the correct answer. (Kudos please if you like the explanation)
Thus, by using formula -
A = P x (1+r)^n,
we know that
6000 = 2000 x (1+r)^6
i.e. 3 = (1+r)^6
Let's call term (1+r) = a
Thus, we can rewrite the above equation as
3 = a^6
Thus, a = 3 ^ (1/6) ......... (Let's call it as Result I)
Now, question is by which year end, Roxie will earn total interest of 52,000 i.e. when will total outstanding be 2000 + 52000 = 54000?
By using formula, we can write -
54000 = 2000 x (1+r)^n
i.e. 27 = (1+r)^n
now, by substituting 'a' for (1+r), we rewrite above equation as
27 = a^n
i.e. 3^3 = a^n
Thus, a = (3) ^ (3/n) (Let's call it as Result II)
By comparing result I and II above, we know that
3 ^ (1/6) = (3) ^ (3/n)
i.e. 1/6 = 3/n
thus, n = 3 x 6 = 18
Hence, IMO - Option A is the correct answer. (Kudos please if you like the explanation)
