(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
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