question_answer

Arif took a loan for Rs. 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

(a) Compounded annually.

(b) Compounded half yearly.

Answer:

(a) Compounded annually

P = Rs. 80000, T = \[1\frac{1}{2}\]year

R = 10% of p.a. and 5% of half years

A = P \[{{\left( 1+\frac{R}{100} \right)}^{n}}\]

\[=80000{{\left( 1+\frac{10}{100} \right)}^{1}}{{\left( 1+\frac{5}{100} \right)}^{1}}\]

\[=80000\left( \frac{11}{10} \right)\left( \frac{21}{20} \right)\]

A = Rs. 92400

(b) Compounded half yearly.

P = Rs. 80,000, R = 10%

\[=\frac{10}{2}=5%\]

\[n=1\frac{1}{2}\]year \[=\frac{3}{2}\times 32=3\]half years

A = P \[{{\left( 1+\frac{R}{100} \right)}^{n}}\]

\[=80,000{{\left( 1+\frac{5}{100} \right)}^{3}}\]

\[A=80,000{{\left( \frac{21}{20} \right)}^{3}}\]

\[=80,000\times \frac{21}{20}\times \frac{21}{20}\times \frac{21}{20}\]

A = Rs 92610

Difference in amounts = Rs. 92610 - Rs.92400

= Rs. 210