At the beginning of the year 2014, a person invested some amount in the bank at a certain rate of interest per annum, compounded annually.At the beginning of the year 2018, the accumulated interest was Rs.40,000 and at the beginning of the year 2022, the accumulated interest became Rs.90,000.What was the principal amount invested?
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Answer:
At the beginning of the year 2014, a person invested some amount in the bank at a certain rate of interest per annum, compounded annually.At the beginning of the year 2018, the accumulated interest was Rs.40,000 and at the beginning of the year 2022, the accumulated interest became Rs.90,000.What was the principal amount invested?
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Answer:
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