Question

1
b) 18,000 for 2 1/2 years at 10% per annum compounded annually.
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Answer 1

$\huge\bf\boxed{\boxed{\underline{\red{Question!!}}}}$

18,000 for 2 $\frac{1}{2}$ years at 10% per annum compounded annually.

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$\huge\bold{Given}$

$\huge\mathrm\orange{Prinicipal \:(P) = 18,000}$

$\huge\mathrm\orange{T = 2 \frac{1}{2}}$

$\huge\mathrm\orange{R = 10 \:percentage}$

Here we take 2 $\frac{1}{2}$ as

Compound interest of 2 year + simple interest of $\frac{1}{2}$ year

$\huge\mathrm\pink{\:Compund \:interest \:of \:2 \:year}$

So by using formula

$\huge\bf\boxed{\boxed{\underline{\red{A = P +(1+\frac{R}{100})^{n}}}}}$

$\huge\mathrm\pink{\:Substituting \:the \:values}$

➪ A = 18,000 ( 1 + $\frac{10}{100})^{2}$ ( zero zero get cancel)

➪ A = 18,000 ( 1 + $\frac{1}{10})^{2}$

➪ A = 18,000 ( 1 + $\frac{10 + 1}{10})^{2}$ (take L.C.M)

➪ A = 18,000 ( $\frac{11}{10})^{2}$

➪ A = 18,000 × $\frac{121}{100}$

➪ A = 180 × 121

➪ A = 21,780

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{A = 21,780}}}}}}}}}$

Now :

Amount = Principal + Interest

21,780 = 18,000 + interest

21,780 - 18,000 = interest

3780 = interest

i = 3780

Amount = 21,780 interest = 3780

Now the simple interest of $\frac{1}{2}$

$\huge\bold{Given}$

$\huge\mathrm\orange{P = 21 ,780}$

$\huge\mathrm\orange{R = 10 \:percentage}$

$\huge\mathrm\orange{T = \frac{1}{2}}$

So by using formula

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{Interest = \frac{P×R×T}{100}}}}}}}}}}$

➪ $\frac{21780×10×{1}{2}}{2×100}$

➪ $\frac{21780×10}{2×100}$

➪ $\frac{21780}{2}$

➪ $1089$

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{Interest = 1089}}}}}}}}}$

Now the simple interest be :

Compound interest of 2 year + Simple Interest of $\frac{1}{2}$

☞︎︎︎ 3780 + 1089

☞︎︎︎ 4869

Amount = Prinicipal + Interest

☞︎︎︎ A = 18000 + 4869

☞︎︎︎ A = 22869

$\huge\bf\boxed{\boxed{\underline{\red{Amount = 22869}}}}$

$\huge\bf\boxed{\boxed{\underline{\red{Interest = 4869}}}}$