Question

find the amount and the compound interest on rupees 62500 3/ 2 years and 8% per annum compounded half yearly

Answer 1

Answer:

The amount is Rs.70304 and Compound interest is Rs.7804

Step-by-step explanation:

Principal = 62500

Time = 3/2 years

Rate of interest = 8 % = 0.08

Compounded half yearly

No. of compounds per year = 2

Formula : $A=P(1+\frac{r}{n})^{nt}$

$A=62500(1+\frac{0.08}{2})^{2 \times \frac{3}{2}}$

$A=70304$

Interest = Amount - Principal = 70304- 62500=7804

Hence the amount is Rs.70304 and Compound interest is Rs.7804

Answer 2

Answer:

$\red { Compound \: interest} \green {= Rs \:7804 }$

Step-by-step explanation:

$Principal (P) = Rs \:62500$

$Time (T) = \frac{3}{2} \: years = 1\frac{1}{2} \: years$

$Rate \: of \: Interest (r) = 8\% \: per \: annum$

$rate for \:half \: yearly = \frac{1}{2} \times 8\% =4\%$

$As \: interest \: is \: compounded \:half\\yearly, \:so \: number \: of \:conversion \:periods\\in \: 1\frac{1}{2} \: years \: is \: 3, \:So, \: n = 3$

$\boxed { \pink { Amount (A) = P\left( 1 + \frac{r}{100} \right )^{n} }}$

$= 62500 \left( 1 + \frac{4}{100}\right)^{3}\\= 62500 \left( 1 + \frac{1}{25} \right)^{3}\\= 62500 \left( \frac{25+1}{25}\right)^{3}\\= 62500\times \left(\frac{26}{25}\right)^{3}\\= 62500 \times \frac{25}{26} \times \frac{25}{26} \times \frac{25}{26}$

$= Rs\: 70304$

$Compound \: interest = A - P \\= 70304 - 62500 \\= Rs\:7804$

Therefore.,

$\red { Compound \: interest} \green {= Rs \:7804 }$

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