Question

Golu let Polo rupees 32500 purchased a bike at 12.5% per annum if the interest is compounded semi annually find the interest paid by polu after 1 and half years
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Answer 1

AnswEr :

$\bf{\dag}\:\:\underline{\textsf{Rate Halved \& Time Twice in Semi Annually :}}\\\\\bullet\:\:\textsf{Principal = Rs. 32500}\\\\\bullet\:\:\sf{Rate =12.5\%=\dfrac{1}{8}=\dfrac{1}{8 \times 2}=\dfrac{1}{16}}\\\\\bullet\:\:\sf{Time=1{}^{1}\!/{}_{2}=\dfrac{3}{2}=\dfrac{3}{2} \times 2=3}$

$\rule{160}{1}$

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\tt CI = P\bigg\lbrack\left(1+\dfrac{r}{100}\right)^{t}-1\bigg\rbrack\\\\\\:\implies\tt CI = 32500 \times \bigg\lbrack\left(1+\dfrac{1}{16}\right)^{3}-1\bigg\rbrack\\\\\\:\implies\tt CI = 32500\times \bigg\lbrack\left(\dfrac{17}{16}\right)^{3}-1\bigg\rbrack\\\\\\:\implies\tt CI = 32500 \times \bigg\lbrack\dfrac{4913}{4096}-1\bigg\rbrack\\\\\\:\implies\tt CI = 32500 \times \bigg\lbrack\dfrac{4913 - 4096}{4096}\bigg\rbrack\\\\\\:\implies\tt CI =32500 \times\dfrac{817}{4096}\\\\\\:\implies\tt CI =7.934 \times 817\\\\\\:\implies\underline{\boxed{\tt CI =Rs.\:6482.54}}$

⠀

$\therefore\:\underline{\textsf{Polu will give Interest of \textbf{Rs. 6482.54} to Golu.}}$

Answer 2

Answer:

Amount Lent = Rs 32500

Rate of interest = 12.5 % per annum

= 6.25 % Half Yearly (semi - Annually)

Time = 3/2 years = 3  Half Years

⇒ Amount = P (1 + R/100)ⁿ

⇒ Amount = 32500 ( 1  + 6.25/100)³

⇒ Amount =  Rs. 38,982.54

Interest Paid = 38,982.54 - 32500

= Rs 6,482.54