Question

find the amount and the compound interest on Rs 10000 for 1 and half years at 10% per annum compounded half yearly​

Answer 1

Answer:

Amount= RS 11576.25

C.I  = Rs 1576.25

Step-by-step explanation:

Answer 2

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf\large \underbrace{\underline{ Understanding \: compound \: intereste }}$

Compound interest is the addition of interest to the principal sum of loan or deposit. it's a result of reinventing intereste, rather than paying it out ,so the interest in the next period is than earned on the principal sum + previously accumulated intereste.

$\\ \color{purple}\large\sf \underline{ \: Question :- }$

Find the amount and the compound interest on Rs 10000 for 1 and half years at 10% per annum compounded half yearly.

$\\ \color{purple}\large\sf \underline{ \: Solution :- }$

The total accumulated amount A , on the principal sum P + compound interest I ,

We know following formula :-

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \underline{\boxed{\sf \: A = P { \brace {1 + \frac{r}{n} }} ^{nt} }} \\ \\ \sf \: in \: this \: , \:\bold{A} = Amount \: obtained \: \\ \sf \: \:\bold{t } \: is \: the \: numbe r \: of \: years , \: \bold{ r } \: is \: the \: rate \\ \sf\:\bold{ p } \: is \: the \: principal \: \bold{n }\: is \: the \: \: \: number \: of \: \: times \: the \: interest \: given \: in \: year \:$

$\\ \\ \sf \: \: The \: total \: compound \: interest \: generated \: is \: given \\ \underline{\sf by: I = A - P }$

$\\ \sf \: Now , \: we \: have \: been \: given \: that \:$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \green{\rm \: P = Rs \: 10000 \: \: \: and \: \: \: r = 10 \%}$

$\\ \sf \: Therefore \: amount \: credited \: in \: 1 \: year \:$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: A = \: 10000 \times { (1 + \frac{10}{2 \times 100} )} ^{2 \times 1}$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 10000 \times { (1 + \frac{5}{100} )} ^{2 }$

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: 10000 \times { ( \frac{105}{100} )} ^{2 }$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: { ( {105})} ^{2 }$

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: : \implies \: \underline{\boxed{\frak \color{navy} { {11025}}} }$

$\\ \sf \: Also, \: compound \: interest \: will \: be$

$\\ \: \: \: \: \: \: \: \: \: \: \: {\sf I = A - P }$

$\\ \: \: \: \: \: \: \: \: \: \longrightarrow \sf11025 \: - \: 10000 \\ \\ \: \: \: \: \: \: \: \: \: \longrightarrow \sf \underline{ 1025}$

Hence ,

$\\ \bold{\underline{ \: \: The \: amount \: and \: interest \: is \: Rs \: .11025 \: and \: Rs.1025 \: respectively. \: \: \: }}$