Question

calculate the amt and interest on a sum of88000 invested for 1 year at 5% rate of interest p.a compounded half yearly​

Answer 1

AnswEr :

$\bold{Given} \begin{cases} \underline{ \footnotesize\sf{ \star \: \: Compounded\: Half \: Yearly}} \\ \sf{Principal=Rs. 88000} \\ \sf{Rate=5 = \dfrac{5}{2} = 2.5 \% \: p.a.} \\ \sf{Time=1\: Yr. \times 2 = 2}\end{cases}$

• First we will calculate Amount :

$\Longrightarrow \sf{Amount = P \times \bigg(1 + \dfrac{r}{100} \bigg)^{t} }$

$\Longrightarrow \sf{Amount = 88000 \times \bigg(1 + \cancel\dfrac{2.5}{100} \bigg)^{2} }$

$\Longrightarrow \sf{Amount = 88000 \times \bigg(1 + \dfrac{1}{40} \bigg)^{2} }$

$\Longrightarrow \sf{Amount = 88000 \times \bigg(\dfrac{40 + 1}{40} \bigg)^{2} }$

$\Longrightarrow \sf{Amount = 88000 \times \bigg(\dfrac{41}{40} \bigg)^{2} }$

$\Longrightarrow \sf{Amount = \cancel{88000} \times\dfrac{41}{\cancel{40}}\times \dfrac{41}{ \cancel{40}}}$

$\Longrightarrow \sf{Amount =55 \times 41 \times 41}$

$\Longrightarrow \boxed{ \sf{Amount = Rs. \: 92455}}$

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• Now we will calculate Interest :

⇝ Amount = Interest + Principal

⇝ 92455 = Interest + 88000

⇝ Interest = 92455 - 88000

⇝ Interest = Rs. 4455

⠀

∴ Amount is Rs.92455 and Interest is Rs.4455 when compounded Half Yearly.

Answer 2

$\LARGE\underline{\underline{\sf \red{G}\blue{i}\green{v}\orange{e}\red{n}:}}$

• Principal = 88000
• Time = 1 year
• Rate = 5% compounded Half yearly.....

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$

• Amount
• Compound interest ....

$\LARGE\underline{\underline{\sf \red{S}\blue{o}\green{l}\orange{u}\pink{t}\purple{i}\orange{o}\red{n}:}}$

we know that when rate is compounded half yearly, our time will be two times and rate will be Half ..

so,

Time = 2 years

Rate = 2.5%

Now,

$\huge\red{\boxed{\sf A\:=\:P( 1 + \frac{r}{100})^{t}}}$

$A = 88000(1 + \frac{2.5}{100})^{2} \\ \\ A = 88000( \frac{41}{40})^{2} \\ \\ A = \: \frac{ \cancel{88000} \times 41 \times 41}{ \cancel{40 \times 40}} = 92455$

Compound interest = Amount - Principal

$CI = 92455 - 88000 = 4455$

So, we will get, 4455 as interest and 92455 Total Rs.