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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