Question

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

Answer 1

Given:

• Principal (P) = 2000
• Rate of Interest (R%) = 10%
• Amount (A) = 2420

To find:

• Time (n) = ?

The formula to find the amount (A)

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

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

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

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

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

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

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

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

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

Now bases are same, we can compare the exponents,

⇒ 2 =  n

Hence,

• Time (n) = 2 years

Answer 2

Answer:

Answer- 2 years

Step-by-step explanation:

2420=2000(1+10/100)n

2420=2000(11/10)n

(11/10)n=2400/2000

(11/10)n=121/100

(11/10)n=(11/10)2

Answer- 2 years