Question

find compound interset on rs 62500 at 8%for 1 1/2years if the interest is compounded semi anually
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Answer 1

Solution:

Given:

=> Principal amount (P) = Rs. 62500

=> Rate (r) = 8%

=> Time (t) = $\sf{1\dfrac{1}{2}\;years}$

To find:

=> Compound interest

Formula used:

$\sf{\implies A = P\bigg(1+\dfrac{r/2}{100}\bigg)^{2t}}$

Now, first we will find Amount.

$\sf{\implies A = P\bigg(1+\dfrac{r/2}{100}\bigg)^{2t}}$

$\sf{\implies A = P\bigg(1+\dfrac{r}{200}\bigg)^{2t}}$

$\sf{\implies A = 62500\bigg(1+\dfrac{8}{200}\bigg)^{3}}$

$\sf{\implies A = 62500\bigg(\dfrac{200+8}{200}\bigg)^{3}}$

$\sf{\implies A = 62500\bigg(\dfrac{208}{200}\bigg)^{3}}$

$\sf{\implies A = 62500\times (1.04)^{3}}$

$\sf{\implies A = 62500\times 1.124864}$

$\sf{\implies A = Rs.\;70304}$

Now, we will find the compound interest.

=> Compound interest = Amount - Principal amount

=> Compound interest = 70304 - 62500

=> Compound interest = Rs. 7804

Hence, Compound interest = Rs. 7804

Answer 2

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

${\bold{\therefore Compound\:interest=7,804}}$

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

$\underline \bold{Given :} \\ \implies Principal(P) = 62500 \: rupees \\ \\ \implies Rate (R)= 8 \\ \\ \implies Time(t) = 1\frac{1}{2} \: years \\ \\ \underline \bold{To \: Find :} \\ \implies Compound \: interest \: for \: semi \: annual = ?$

• According to given question :

$\bold{Using \: formula \: of \: compounded \: annualy : } \\ \implies A = P(1 + \frac{ \frac{R}{2} }{100})^{2t} \\ \\ \implies A= 62500(1 + \frac{8}{200})^{(2 \times \frac{3}{2}) } \\ \\ \implies A = 62500(\frac{25 + 1}{25} ) ^{3} \\ \\ \implies A= 62500 \times \frac{26}{25} \times \frac{26}{25} \times \frac{26}{25} \\ \\ \implies A= 4 \times 26 \times 26 \times 26 \\ \\ \bold{\implies A =70 ,304} \\ \\ \bold{For \: C.I: } \\ \implies C.I = A- P \\ \\ \implies C.I = 70304 - 62500 \\ \\ \bold{\implies C.I = 7 ,804}$