Question

karan borrowed ₹15,625 at the rate of 16% per annum. find the amount that he has to pay at the end of 9 months if the interest is calculated quarterly .

Answer 1

Hi friend!

Amount when interest is calculated quarterly =
$P(1 + \frac{R}{400})^{4n}$
P = ₹15625
n = 9 months = 9/12 year(s) = 3/4 year(s)
R = 16% p.a.

4n = 3/4 × 4 = 3

$A = P(1 + \frac{16}{400} )^{4n} \\ \\ A = 15625(1 + \frac{16}{400} ) ^{3} \\ = 15625(1 + \frac{1}{25} ) ^{3} \\ = 15625( \frac{25 + 1}{25} ) ^{3} \\ = \frac{15625 \times 26 \times 26 \times 26}{25 \times 25 \times 25} \\ = \frac{1 \: \sout{25} \: \sout{625} \: \sout{15625} \times 26 \times 26 \times 26}{1 \: \sout{25} \times {\sout{25}}^{1} \times \sout{25} \: 1} \\ = 26 \times 26 \times 26 \\ = 17576$
Amount = ₹17576

Therefore, Karan has to pay ₹17576 at the end of 9 months.

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