Question

6. In what time sum of 2000 will become ? 2420, if the interest rate is 10%, compounded annually​

Answer 1

Answer:

Given:

Principal (P) = 2000

Rate of Interest (R%) = 10%

Amount (A) = 2420

To find:

Time (n) = ?

The formula to find the amount (A)

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

$\implies \bf 2420=2000(1+\frac{R}{100})^{n}⟹2420=2000(1+100R)n$

$\implies \bf \frac{2420}{2000}=(1+\frac{R}{100})^{n}⟹20002420=(1+100R)n$

$\implies \bf \frac{242}{200}=(1+\frac{1}{10})^{n}⟹200242=(1+101)n$

$\implies \bf \frac{242}{200}=(\frac{10+1}{10})^{n}⟹200242=(1010+1)n$

$\implies \bf \frac{242}{200}=(\frac{11}{10})^{n}⟹200242=(1011)n$

$\implies \bf \frac{2\times 11\times 11}{2\times10 \times 10}=(\frac{11}{10})^{n}⟹2×10×102×11×11=(1011)n$

$\implies \bf \frac{11\times 11}{10\times 10}=(\frac{11}{10})^{n}⟹10×1011×11=(1011)n$

$\implies \bf (\frac{ 11}{ 10})^{2}=(\frac{11}{10})^{n}⟹(1011)2=(1011)n$

Now bases are same, we can compare the exponents,

⇒ 2 =  n

Hence,

Time (n) = 2 years

Answer 2

p = Rs. 2000, A = Rs.2420, R = 10% , N = ?

= 2420 = 2000(1+10/100) ^N

= (11/10)² = (11/10)^N

= N = 2 years.

Hope it will help you...