Find the amount and the compound interest on Rs 160000 for 2 years

Question:

Find the amount and the compound interest on Rs 160000 for 2 years at 10% per annum, compounded half-yearly.

Solution:

Principal, $P=$ Rs. 160000

Annual rate of interest, $R=10 \%$

Rate of interest for a half year $=\frac{10}{2} \%=5 \%$

Time, $n=2$ years $=4$ half years

Then the amount with the compound interest is given by

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

$=160000 \times\left(1+\frac{5}{100}\right)^{4}$

$=160000 \times\left(\frac{100+5}{100}\right)^{4}$

$=160000 \times\left(\frac{105}{100}\right)^{4}$

$=160000 \times\left(\frac{21}{20}\right) \times\left(\frac{21}{20}\right) \times\left(\frac{21}{20}\right) \times\left(\frac{21}{20}\right)$

$=(21 \times 21 \times 21 \times 21)$

$=$ Rs 194481

Therefore, compound interest $=$ amount $-$ principal $=\mathrm{Rs}(194481-160000)=\mathrm{Rs} 34481$

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