Question

Find the difference between the interest on:
a) A sum of ₹20000 deposited in a bank for 2 years@ 10% compounded annually.
b) A sum of ₹20000 deposited in a bank for 2 years @ 10% simple interst.
Which one is greater and why​

Answer 1

Step-by-step explanation:

Given :-

a) A sum of ₹20000 deposited in a bank for 2 years@ 10% compounded annually.

b) A sum of ₹20000 deposited in a bank for 2 years @ 10% simple interst.

To find :-

Find the difference between the two Interests ?

Which one is greater and why ?

Solution:-

a)

Given sum deposited in the bank = ₹20000

Time = 2 years

Rate of Interest = 10%

We know that

Amount = P[1+(R/100)]^n

=> A = 20000[1+(10/100)]²

=> A = 20000[1+(1/10)]²

=> A = 20000[(10+1)/10]²

=> A = 20000[11/10]²

=>A = 20000×121/100

=> A = 200×121

=> A = 24200

Amount = ₹ 24,200

We know that

Amount = Principle + Interest

=> Interest = A-P

=> CI = 24200-20000

=> CI = 4200

=> Compound Interest = ₹4200-----(1)

b)Given sum deposited in the bank = ₹20000

Time = 2 years

Rate of Interest = 10%

We know that

Simple Interest =PTR/100

=> SI = 20000×2×10/100

=> SI = 200×2×10

=> SI = 4000

Simple Interest = ₹ 4000 ---------(2)

From (1) &(2)

Compound Interest > Simple Interest

Simple interest is based on principal amount and it is the same for all number of years whereas compound interest is based on the principal amount and the interest compounded for a cycle of the period and it is not same for all number of years

₹4200 > ₹ 4000

The difference between CI and SI

=> 4200-4000

=> ₹ 200

Therefore, difference = ₹ 200

Answer:-

1)

The difference between the two interests is ₹ 200

2)

Compound interest is greater than the Simple Interest for the given problem.

Reason :-

Simple interest is based on principal amount and it is the same for all number of years whereas compound interest is based on the principal amount and the interest compounded for a cycle of the period and it is not same for all number of years

Used formulae:-

• Amount = P[1+(R/100)]^n

• Simple Interest =PTR/100

• Amount = Principle + Interest

• P = Principle

• T = Time

• R = Rate of Interest

• n = Number of times the interest calculated