Question

at what rate of compound interest per annum will a sum of rupees 2000 become rupees 2332.80 in 2 years, interest compounded annually?

Answer 1

Given, Principal = 2000, A = 2332.80, Time n = 2 years.

We know that A = P(1 + r/100)^n

⇒ 2332.8 = 2000(1 + r/100)^2

⇒ 2332.8/2000 = (1 + r/100)^2

⇒ √2332.8/2000 = (1 + r/100)

⇒ 27/25 = 1 + r/100

⇒ 27/25 - 1 = r/100

⇒ 2/25 = r/100

⇒ r = 8.

Therefore, R = 8%.

Hope it helps!

Answer 2

Hi there!
Here's the answer:

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¶¶¶ Points to remember :

When Interest is compounded Annually,

$Amount = P (1 + \frac{R}{100})^{n}$

where, P = Principal
Rate = R% per annulment
Time = n years

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SOLUTION :

Given:
Compound Interest on a sum of 2000₹ at a certain rate of interest compounded annually for 2 years is 2332.80₹

Amount = Compound Interest = 2332.80₹
Principal P = 2000₹
Time n = 2 years
let rate per annum = r%

Substitute in Formula

$2332.80 = 2000( 1 + \frac{R}{100})^{2}$

=> $\frac{2332.80}{2000} = (1 + \frac{R}{100})^{2}$

=> √(2332.80/2000) = $(1 + \frac{R}{100})$

=> $(1 + \frac{R}{100}) = \frac{27}{25}$

=> $\frac{R}{100} = \frac{2}{25}$

=> $\frac{R}{4} = 2$

=> $R = 4×2$

=> $R = 8$

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$\underline{\underline{Required\: Rate = 8\%}}$

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Hope it helps