Question

find the amount and the compound interest on ₹12800 for 1 year at7 1/2%per annum,compounded semi annually​

Answer 1

step by step:-

aby answer

Answer 2

Hi,let's Start .

$\rm \huge\dag \huge\underline{Given: }$

Principal = ₹ 12800, Time ( T) = 1 year.

$\rm\large{ \: year \: rate \: \: of \: interest \: = \: 7 \frac{1}{2} \%} \: \: \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \rm \large{ = \frac{15}{2} \%}$

$\rm \large{ rate \: of \: interest\: semi \: annually} \\ \rm \large R = \frac{1}{2} \: \times \: \frac{15}{2} \\ \\ \rm \large = \frac{15}{4}\%$

$\rm \huge\dag\underline{To \: find: }$

Amount = ? , Compound interest = ?

$\rm\huge\dag\underline{Answer: }$

$\rm\large\pink{Amount \: = 13778 \: rupees\: \: and } \: \\ \rm \large \pink{compound \: interest \: = \: 978}$

$\rm\huge\dag\underline{Soluation: }$

$\rm \large \: We \: know \: that , \: \\ \rm \bigstar\large \: \: A = P (1 + \frac{ \:R}{100})^{n}$

$\rm \large \mapsto \green{ (\: 12800 \: + \: \frac{ \frac{15}{4} } {100 }) ^{2} }$

$\rm \large \mapsto \green{ \: 12800( \: 1 \: + \: \frac{400 + 15}{400})^{2} }$

$\rm \large \mapsto \green{ \: 12800 \: \times \: \frac{415 \: \times \: 415}{ \: 400} }$

$\rm \large \mapsto \green{ \: A \: = \: 13778 \: rupees}$

$\rm \bigstar \: \: \large Compound \: interest \: = \: A \: - P \\ \\ \rm \large \mapsto13778 \: - \: 12800 \\ \\ \rm \large \mapsto \: 978 \: rupees$

Hence, Amount = ₹ 13778 and

Compound interest = ₹ 978 .