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

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

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

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

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

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

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

\[A=80000{{\left( \frac{21}{20} \right)}^{3}}\]

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

A =Rs. 92610

Difference in amounts

=Rs. 92610\[-\]Rs.92400

=Rs.210