3 Tutor System
Starting just at 265/hour

# 6. 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 $$1\frac { 1 }{ 2 }$$ years if the interest is (i) compounded annually. (ii) compounded half yearly.

(i) We are given: P = ₹ 80,000 , R = 10% p.a. and n = $$1\frac { 1 }{ 2 }$$ years Since the interest is compounded annually so we have

Simple Interest=$$\frac{P \times R \times n}{100}$$

=$$\frac{80,000\times 10\times 1}{100}$$

=$$₹ \;8,000$$

Principal for the second year=P+SI

=₹ 80,000 + ₹ 8,000 = ₹ 88,000

Now for $$\frac{1}2$$ year we have interest==$$\frac{88,000\times 10\times 1}{100\times 2}=₹ \;4,400$$

Thus, amount=₹ 88,000 + ₹ 4,400=₹ 92,400

(ii)So for compounded interest half yearly we have:

R=$$\frac{10}2=5$$% half yearly.

n=$$1\frac{1}2$$years=$$\frac{3}2\times 2=3$$ half years

∴ Amount=$$P(1+\frac{R}{100})^n$$

=$$80,000(1+\frac{5}{100})^3$$

=$$80,000(\frac{21}{20})^3$$

=$$80,000\times(\frac{21}{20}\times \frac{21}{20}\times \frac{21}{20})$$

=$$10\times 9261$$

=$$₹ \; 92610$$

Difference between the amounts = ₹ 92,610 – ₹ 92,400 = ₹ 210