# Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after \(1{\Large\frac{1}{2}}\) years if the interest is

(i) compounded annually (ii) compounded half-yearly

**Solution:**

Given that, Arif took a loan of ₹ 80,000 from a bank

For Amount and Compound Interest (C.I.)

A = P[1 + (r/100)]^{n}

P = ₹ 80,000

n = \(1{\Large\frac{1}{2}}\) years

R = 10% p.a. compounded half-yearly and 10% p.a. compounded yearly

(i) For calculation of Compound Interest (C.I.) compounded annually:

Since ‘n’ is \(1{\Large\frac{1}{2}}\) years, the amount can be calculated for 1 year, and having that amount as principal, S.I. can be calculated for the remaining 1/2 year because C.I. is always calculated annually.

A = P[1 + (r/100)]^{n}

A = 80000[1 + (10/100)]^{1}

A = 80000 × 11/10

A = 80000 × 1.1

A = 88000

Amount after 1 year = ₹ 88,000

Therefore, the principal for the next 1/2 year = ₹ 88,000

We know that,

Simple interest = PRT/100

Simple Interest(S.I.) for 1/2 years = 88000 × (1/2) × (10/100)

= 8800/2

= 4400

Therefore amount after \(1{\Large\frac{1}{2}}\) years = 88000 + 4400 = ₹ 92400

(ii) For calculation of Compound Interest (C.I.) compounded half-yearly, we will consider rate as 5% p.a. and ‘n’ as 3

A = P[1 + (r/100)]^{n}

A = 80000[1 + (5/100)]^{3}

A = 80000[1 + (1/20)]^{3}

A = 80000 × (21/20)^{3}

A = 80000 × (21/20) × (21/20) × (21/20)

A = 80000 × (9261/8000)

A = 10 × 9261 = ₹ 92610

Therefore, difference in the amount = ₹ 92610 - ₹ 92400 = ₹ 210

**Video Solution:**

## Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, find the difference in amounts he would be paying after \(1{\Large\frac{1}{2}}\) years if the interest is (i) Compounded annually (ii) Compounded half-yearly

### Maths NCERT Solutions Class 8 - Chapter 8 Exercise 8.3 Question 6

**Summary:**

Arif took a loan of ₹ 80,000 from a bank. If the rate of interest is 10% per annum, the difference in amounts he would be paying after \(1{\Large\frac{1}{2}}\) years if the interest is (i) Compounded annually (ii) Compounded half-yearly is ₹ 92610 - ₹ 92400 = ₹ 210