Under compound interest compounded annually, a sum becomes Rs.999 in 9 years and Rs. 2997 in 12
years. Find the principal?
A] Rs. 37
B] Rs. 111
C] Rs. 333 D] None of these
Answers
Given :- Under compound interest compounded annually, a sum becomes Rs.999 in 9 years and Rs. 2997 in 12 years. Find the principal ?
A] Rs. 37
B] Rs. 111
C] Rs. 333
D] None of these.
Solution :-
we know that,
- Amount(A) = P[1 + (R/100)]^(time)
Let us assume that , given Principal is Rs.P and rate of interest is R% per annum compounded annually.
given that amount after 9 year is Rs.999.
So,
→ 999 = P[1 + (R/100)]⁹ -------- Eqn.(1)
also, given that, amount after 12 years is Rs.2997.
So,
→ 2997 = P[1 + (R/100)]¹² ------- Eqn.(2) .
Dividing Eqn.(2) by Eqn.(1) we get,
→ (2997/999) = P[1 + (R/100)]¹² / P[1 + (R/100)]⁹
→ 3 = [1 + (R/100)]³
Putting this value in Eqn.(1) , we get,
→ 999 = P[1 + (R/100)]⁹
→ 999 = P * [ {1 + (R/100)}³ ]³
→ 999 = P * (3)³
→ 999 = 27P
dividing both sides by 27,
→ P = Rs.37 (Ans.) (Option A).
Hence, Required Principal is Rs.37.
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