In the beginning of the year 2001, Mr. X invest some amount in a bank, In the beginning of 2004, the accumulated interest is Rs. 10000 and in the beginning of 2007, the accumulated interest becomes Rs. 25000. The interest rate is compounded annually and annual interest rate is fixed. The principle amount is:
In the beginning of the year 2001, Mr. X invest some amount in a bank, In the beginning of 2004, the accumulated interest is Rs. 10000 and in the beginning of 2007, the accumulated interest becomes Rs. 25000. The interest rate is compounded annually and annual interest rate is fixed. The principle amount is:
1). 16000
2). 25000
3). 24000
4). 20000
1 answers
Let the principle amount be P and rate of interest be r.
From the beginning of 2001 and beginning of 2004, there will be accumulated interest of 3 yrs.
So, we can write,
⇒ P (1 + r/100)3 = P + 10000 ---- (1)
Similarly, from the beginning of 2001 and beginning of 2007, there will be accumulated interest of 6 years.
We can write,
⇒ P (1 + r/100)6 = P + 25000 ----- (2)
Let, (1 + r/100)3 = A
We can write, equation (1) as,
⇒ P ? A = P + 10000
⇒ P (A – 1) = 10000 ---- (3)
Similarly, we can write equation (2) as,
⇒ P × A2 = P + 25000
⇒ P (A2 – 1) = 25000
⇒ P (A – 1) (A + 1) = 25000 ----- (4)
Dividing equation (4) by equation (3), we get,
⇒ A + 1 = 5/2
⇒ A + 1 = 2.5
⇒ A = 1.5
Putting A = 1.5 in eq (3), we get,
⇒ P × (1.5 - 1) = 10000
∴ P = 20000