Question

Find the difference between the compound interest compounded yearly and half yearly on rs10000 for 18months at 10% per annum
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Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Difference=26.25\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given: }} \\ \tt: \implies Principal(p) = 10000\:rupees \\ \\ \tt: \implies Time(t) = 18 \:months\\ \\ \tt: \implies Rate\%(r) = 10\% \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies C.I\:half\:yearly- C.I\:annualy=?$

• According to given question :

$\bold{As \: we \: know \: that(For \: 1 \: year)} \\ \tt: \implies A =p(1 + \frac{r}{100} )^{t} \\ \\ \tt: \implies A= 10000 \times (1 + \frac{10}{100} )^{1} \\ \\ \tt: \implies A= 10000 \times 1.1 \\ \\ \green{\tt: \implies A = 11000 \: rupees} \\ \\ \bold{For \: next \: 6 \: months : } \\ \tt: \implies Interest = \frac{11000 \times 10 \times 6}{12 \times 100} \\ \\ \green{\tt: \implies Interest = 550 \: rupees} \\ \\ \bold{For \: Compoud \: interest : } \\ \tt: \implies C.I_{1} = a + interest - p \\ \\ \tt: \implies C.I_{1}= 11000 + 550 - 10000 \\ \\ \green{\tt: \implies C.I_{1}= 1550 \: rupees}$

$\bold{As \: we \: know \: that} \\ \tt: \implies A= p(1 + \frac{ \frac{r}{2} }{100} ) ^{2t} \\ \\ \tt: \implies A = 10000 \times (1 + \frac{10}{2 \times 100} )^{3} \\ \\ \tt: \implies A= 10000 \times (1 + 0.5)^{3} \\ \\ \tt: \implies A = 10000 \times (1.05)^{3} \\ \\ \tt: \implies A= 10000 \times 1.157625 \\ \\ \green{\tt: \implies A=11576.25 \: rupees} \\ \\ \bold{For \: compound \: interest : }\\ \tt: \implies C.I_{2}= A - p \\ \\ \tt: \implies C.I_{2}= 11576.25 - 10000 \\ \\ \green{\tt: \implies C.I_{2}= 1576.25 \: rupees} \\ \\ \bold{For \: Difference : } \\ \tt: \implies Difference= C.I_{2}- C.I_{1}\\ \\ \tt: \implies Difference = 1576.25- 1550 \\ \\ \green{\tt: \implies Difference= 26.25 \: rupees}$