Question

What is the difference between the compound interests on rs.12000 at 20%p.a for one year when compounded yearly and half yearly?

Answer 1

Heya ✋

Given that

P = ₹12,000

R = 20 % p.a.

T = 1 year

Solution

When the interest is compounded annually

C.I. = P{(1+R/100)^n - 1}

= 12,000{(1+20/100) - 1}

= 12,000{(100+20/100) - 1}

= 12,000{(120/100) - 1}

= 12,000{6/5 - 1}

= 12,000{6 - 5/5}

= 12,000 × 1/5

= ₹2,400

When the interest is compounded half - yearly

A = P(1+R/200)^2n

= 12,000(1+20/200)^2 × 1

= 12,000(200+20/200)^2

= 12,000(220/200)^2

= 12,000(11/10)^2

= 12,000 × 121/100

= ₹14,520

C.I. = A - P

= ₹(14,520 - 12,000)

= ₹2,520

Difference = (C.I. for half - yearly) - (C.I. for annually)

= ₹(2,520 - 2,400)

= ₹120






Thanks :))))