Xavier Aptitude Test 2015 Paper

Question : 65 of 113

Marks: +1, -0

In the beginning of the year 2004, a person invests some amount in a bank. In the beginning of 2007, the accumulated interest is Rs.10,000 and in the beginning of 2010, the accumulated interest becomes Rs.25,000. The interest rate is compounded annually and the annual interest rate is fixed. The principal amount is:

Rs. 16,000
Rs. 18,000
Rs. 20,000
Rs. 25,000
None of the above

Validate

Solution:

Let Principal amount = x and annual interest rate =100%
∴ x (1 + r)

^{3}

= x + 10000 and x (1 + r)

^{6}

= x + 25000
From the start of 2004 to the start of 2007, time period = 3 years and from the start of 2004 to the start of 2010, time period.
Put (1 + r)

^{3}

= a
Then, xa = x + 10000 and xa

^{2}

= x + 25000

\⇒x(a-1)=10000

.............(i)
And

x\ (a^{2}-1\ )=25000

.............(i)

x(a+1)(a-1)=25000

...............(ii)
an dividing (ii) by (i), we get
a + 1 =

25000/10000

= 2.5
⇒ a = 1.5
Now from equation (i),
x =

10000/0.5

= 20000.

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