Question

simple interest on a sum of money for 2 years at 4% is 450. find compound interest on the same sum and at the same rate for 2 years.​

Answer 1

Given :-

• Simple interest (S.I.) on a sum of money = 450 Rs
• time period , t = 2 years
• rate of interest , R = 4 %

To find :-

• Compound interest (C.I.) on the same sum of money at the same rate and for the same time of 2 years.

Formula required :-

• Formula for calculating Simple interest

$\red{\bigstar}\boxed{\sf{S.I.=\frac{P\times R\times t}{100}}}$

(where P is the principle , t is the time and R is the rate of interest )

• Formula for calculating Compound interest

$\red{\bigstar}\boxed{\sf{C.I.=P\left(1+\dfrac{R}{100}\right)^{t} - P}}$

(where P is the principle , t is the time and R is the rate of interest)

Solution :-

Calculating Principle money Using Formula for S.I.

$\implies\sf{S.I.=\dfrac{P\times R\times t}{100}}\\\\\implies\sf{450=\dfrac{P\times 4 \times 2}{100}}\\\\\implies\sf{P=\dfrac{45000}{4\times2}}\\\\\implies\boxed{\sf{P=5625\;\;Rs}}$

Now calculating C.I. on P = 5625 Rs , R = 4 % , t = 2 yrs

$\implies\sf{C.I.=P\left(1+\dfrac{R}{100}\right)^t-P}\\\\\implies\sf{C.I.=5625\left( 1 + \dfrac{4}{100}\right)^2-5625}\\\\\implies\sf{C.I.=5625\left(1+\dfrac{16}{10000}+\dfrac{8}{100}\right)-5625}\\\\\implies\sf{C.I.=5625\left(1+\dfrac{16}{10000}+\dfrac{8}{100}-1\right)}\\\\\implies\sf{C.I.=5625\left(\dfrac{16+800}{10000}\right)}\\\\\implies\sf{C.I.=\dfrac{5625\times 816}{10000}}\\\\\implies\sf{C.I.=\dfrac{4590000}{10000}}\\\\\implies\red{\underline{\boxed{\sf{C.I.=459\;\;Rs}}}}$

Hence,

Compound interest on the same amount , at the same rate and for same time of 2 years is 459 Rs.