Question

In how many years will ₹20000 amount to ₹21632 at 4% p.a. compounded annually?

Answer 1

Solution :

$\underline{\bf{Given\::}}}$

• Principal, (P) = Rs.20000
• Amount, (A) = Rs.21632
• Rate, (R) = 4%

$\underline{\bf{To\:find\::}}}$

The time of the compound Interest.

$\underline{\bf{Explanation\::}}}$

We know that formula of the compound annually;

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

A/q

$\longrightarrow\sf{21632=20000\bigg(1+\dfrac{4}{100}\bigg)^{n} }\\\\\\\longrightarrow\sf{\cancel{\dfrac{21632}{20000} }=\bigg(1+\cancel{\dfrac{4}{100} }\bigg)^{n} }\\\\\\\longrightarrow\sf{\dfrac{676}{625} =\bigg(1+\dfrac{1}{25} \bigg)^{n} }\\\\\\\longrightarrow\sf{\dfrac{676}{625} =\bigg(\dfrac{25+1}{25} \bigg)^{n} }\\\\\\\longrightarrow\sf{\dfrac{676}{625} =\bigg(\dfrac{26}{25} \bigg)^{n} }\\\\\\\longrightarrow\sf{\bigg(\dfrac{26}{25} \bigg)^{2} ={\bigg(\dfrac{26}{25} \bigg)^{n} }}$

$\longrightarrow\bf{n=2\:years}$

Thus;

The time of the compound annually will be 2 years .

Answer 2

✬ Years = 2 ✬

Step-by-step explanation:

Given:

• Principal (P) is Rs 20000
• Amount (A) is Rs 21632
• Rate (R) is 4% per annum.

To Find:

• What is time (T) ?

Solution: Let the time be n years.

As we know that , Compound Interest formula is

★ Amount = P ( 1 + R/100)^n ★

$\implies{\rm }$ 21632 = 20000 (1 + 4/100)^n

$\implies{\rm }$ 21632 = 20000 (100 + 4/100)^n

$\implies{\rm }$ 21632/20000 = (104/100)^n

$\implies{\rm }$ 10816/10000 = (104/100)^n

$\implies{\rm }$ 104•104/100•100 = (104/100)^n

$\implies{\rm }$ 104²/100² = (104/100)^n

$\implies{\rm }$ (104/100)² = (104/100)^n

$\implies{\rm }$ 2 = n

Hence in two years the sum will be amount to Rs 21,632.