At what rate percent per annum compound interest will Rs 6000 amount to Rs 6945.75 in 3 years?

Calculate the amount and the compound interest on :
Rs. 6,000 in 3 years at 5% per year.

For 1st year,
P = Rs. 6,000; R = 5%, and T = 1 year
∴ Interest = Rs. `[6,000 xx 5 xx 1]/[ 100 ]` = Rs. 300.
And, amount = Rs. ( 6,000 + 300 ) = Rs. 6,300
For 2nd year,
P = Rs. 6,300; R = 5%, and T = 1 year
∴ Interest = Rs. `(6,300 xx 5 xx 1)/100` = Rs. 315
And, amount = Rs. ( 6,300 + 315 ) = Rs. 6,615
For 3rd year,
P = Rs. 6,615; R = 5% and T = 1 year
∴ Interest = Rs. `(6,615 xx 5 xx 1)/100` = Rs. 330.75
And, Amount = Rs. ( 6,615 + 330.75 ) = Rs. 6,945.75
∴ C.I. accrued = Final amount - Intitial Principal
                       = Rs. ( 6,945.75 - 6,000 )
                       = Rs. 945.75

Concept: Concept of Compound Interest - Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

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Solution

Given that: A = ₹6,615 P = ₹6,000 T = 2 years (adsbygoogle = window.adsbygoogle || []).push({}); R = ?When the interest is compounded annually Amount= P(1+R100)n ⇒ 6,615 = 6000[(1+R100)2 ⇒ 6,6156,000= (100+R100)2 ⇒ 441400 = (100+R100)2Taking squareroot on both sides; ⇒ √441400 = 100+R100 ⇒ 2120 = 100+R100 ⇒ 21 × 100 = 20(100+R) (adsbygoogle = window.adsbygoogle || []).push({}); ⇒ 2,100 = 2,000 + 20R ⇒ 2,100 - 2,000 = 20R ⇒ 100 = 20R ⇒ R = 10020 ⇒ R = 5 % p.a.

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