Evaluate compound interest on Rs 9000 at 15% per annum for 2 years 4 months, compounded annually

A lent 5000 Rs. to B for 2 years and 3000 Rs. to C for 4 years on simple interest at the same rate of interest and received 2200 Rs. in all from both as interest. The rate of interest per annum is :
[A]$latex 7\frac{1}{8}\%&s=1$
[B]10%
[C]7%
[D]5%

10%
Let the rate of the interest per annum be r%
According to the question,
$latex \frac{5000\times 2\times r}{100}+\frac{3000\times 4\times r}{100} = 2200&s=1$
$latex => 100r +120r = 2200&s=1$
$latex => 220r = 2200&s=1$
$latex => r = \frac{2200}{220} = 10\%&s=1$
Hence option [B] is the right answer.

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Given:

Present value= ₹ 9000

Interest rate= 10 % per annum

Time=2 years 6 months = (2 + ½) years= 5/2 years

To find the amount we have the formula,

Amount (A) = P (1+(R/100))n

Where P is present value, r is rate of interest, n is time in years.

Now substituting the values in above formula we get,

∴ A = 9000 (1 + 10/100)2 [1 + (1/3 × 10)/100]

⇒ A = 9000 (1+1/10)2 (1+1/30)

⇒ A = 9000 (11/10)2 (31/30)

⇒ A = 9000 × 121/100 × 31/30 = 9 × 121 × 31/3

⇒ A = ₹ 11253

∴ Compound interest = A – P

= 11253 – 6000 = ₹ 2253

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