Question

Find the difference between the simple interest and compound interest on RS 16000 for 3/2 years at 5% per annum,compound interest being reckoned half yearly.

Answer 1

Solution:-
Case 1
Given : P = Rs. 16000, R = 5 %, T = 3/2 years 
Simple Interest = (P*R*T)/100
= (16000*5*3)/(2*100)
Simple Interest = Rs. 1200 
Case 2
Compound Interest
Given : P = Rs. 16000, R = 5 % per annum and compounded half yearly so, rate of interest = 2.5 %
T = 3/2 years = 1 year and one half year = 3 half years
A = P (1 +r/100)ⁿ
= 16000 (1 + 2.5/100)³
= 16000 × 102.5/100 × 102.5/100 × 102.5/100
A = Rs. 17230.25
So, compound interest = 17230.25 - 16000 = Rs. 1230.25
Difference between compound interest and simple interest = 1230.25 - 1200 = Rs 30.25
Answer.

Answer 2

Answer:

Difference between Simple Interest And Compound  Interest is Rs. 30.25

Step-by-step explanation:

Given: Principal, P = Rs. 16000

          Rate of Interest , R = 5% p.a.

          Time = 3/2 years.

To find: Difference between Simple Interest And Compound  Interest.

We know that,

$SI=\frac{P\time R\times T}{100}$

$SI=\frac{16000\times5\times\frac{3}{2}}{100}$

$SI=160\times5\times\frac{3}{2}$

$SI=80\times15$

$SI=1200$

So, Simple Interest, SI = Rs. 1200

Now, For Compound Interest,

R = 5/2% as compounded half yearly

n = number of periods = 2 × 3/2 = 3

So,

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

$A=16000(1+\frac{\frac{5}{2}}{100})^3$

$A=16000(\frac{200+5}{200})^3$

$A=16000\times\frac{205}{200}\times\frac{205}{200}\times\frac{205}{200}$

$A=16000\times\frac{205}{200}\times\frac{205}{200}\times\frac{205}{200}$

A = Rs. 17230.25

⇒ Compound Interest. CI = A - P = 17230.25 - 16000 = Rs. 1230.25

Thus, Difference Between interest = 1230.25 - 1200 = 30.25

Therefore, Difference between Simple Interest And Compound  Interest is Rs. 30.25