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A certain sum amounts to Rs. 1000 after 3 years and Rs. 9000 after 5 years at a certain rate of interest compounded annually. What is the amount after 8 years in rupees?
- A900000
- B100000
- C243000
- D343000
Answer not set
Discussion 1
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CCommunity
Let the principle be P and rate be r.
Total amount after 3 years = 1000
We can write,
⇒ P (1 + r/100)3 = 1000 ------ (1)
Total amount after 5 years = 9000
We can write,
⇒ P (1 + r/100)5 = 9000 ------ (2)
Dividing equation (2) by equation (1), we get,
⇒ (1 + r/100)2 = 9
⇒ (1 + r/100) = 3 ------ (3)
Total amount after 8 years = P (1 + r/100)8
We can write as,
⇒ P (1 + r/100)5 × (1 + r/100)3 ------ (4)
putting the value of equation 2 and 3 in 4 we have
∴ Total amount = 9000 × 33 = 9000 × 27 = 243000
Total amount after 3 years = 1000
We can write,
⇒ P (1 + r/100)3 = 1000 ------ (1)
Total amount after 5 years = 9000
We can write,
⇒ P (1 + r/100)5 = 9000 ------ (2)
Dividing equation (2) by equation (1), we get,
⇒ (1 + r/100)2 = 9
⇒ (1 + r/100) = 3 ------ (3)
Total amount after 8 years = P (1 + r/100)8
We can write as,
⇒ P (1 + r/100)5 × (1 + r/100)3 ------ (4)
putting the value of equation 2 and 3 in 4 we have
∴ Total amount = 9000 × 33 = 9000 × 27 = 243000