Question

find the difference between compund interest in Rs.15000 for 2 years at 20%pa when compounded annually and semi annually​

Answer 1

Answer:

The required difference is 345

Step-by-step explanation:

Given

• Principal amount, P = 1500
• Time, T = 2 years
• Rate of interest, R = 20% /annum

• We are supposed to find the difference between compund interest in Rs.15000 for 2 years at 20%pa when compounded annually and semi annually.
• We will use the following formulas:-

• $\leadsto$ A = P $\large(1 + \frac{R}{100} ) {}^{T}$ (for annually)

• $\leadsto$ A = P $\large ({1 + \frac{ \frac{R}{2} }{100} )}^{T}$ (for semi annually)

• $\leadsto$ C.I = A - P

Let's proceed!!

Case 1 (for annually)

A = P $(1 + \frac{R}{100} ) {}^{T}$

A = 1500 $\large(1 + \frac{20}{100} ) {}^{2}$

A = $\large 1500 \: ( \frac{120}{100} ) {}^{2}$

A = 2160

$C.I_1$ = A - P

$\implies$ $C.I_1$ = 2160 - 1500

$\implies$ $C.I_1$ = 660

Case 2 ( for semi annually)

A = P $({1 + \frac{ \frac{R}{2} }{100} )}^{T}$

A = 1500 $\large({1 + \frac{ \frac{20}{2} }{100} )}^{2}$

A = 1500 $\large ( { \frac{220}{200} )}^{2}$

A = 1815

$C.I_2$ = A - P

$\implies$ $C.I_2$ = 1815 - 1500

$\implies$ $C.I_2$ = 315

Now,

The required difference = $C.I_1 - C.I_2$

$\implies$ 660 - 315

$\implies$ 345