Question

Find the amount which Ram will get on Rs. 4096, if he gave it for 18 months at 12 ½% per annum compound half yealy​

Answer 1

Given:

• Ram deposits Rs.4096, if he gave it for 18 months at 12 ½% per annum compound half yealy

To Find:

• The amount he gets back on the money he gave

Solution:

★ when compounded half yearly,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: { \dag \bigg[ \bf \: A = P \bigg(1 + \frac{r}{200} \bigg) {}^{2n} \bigg]}$

★ Where,

• A = Amount
• P = Principal
• R = Rate of interest ( P.A )
• N = Time ( yearly)

★ Here,

• Principal = Rs.4096
• Rate of interest = 12 ½ %
• Time = 1½years( 18 months)

${ \bf{ \underline{ \bigstar \:Substituting \: the \: values : }}}$

$\\ { { : \implies}\bf \: A = P \bigg[1 + \frac{r}{200} \bigg] {}^{2n} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { { : \implies}\bf \: A = 4096 \bigg[1 + \frac{12 \frac{1}{2} }{200} \bigg] {}^{2 \times 1 \frac{1}{2} } } \: \: \: \: \: \: \: \: \: \\ \\ \\ { { : \implies}\bf \: A = 4096 \bigg[1 + \frac{ \dfrac{25}{2} }{200} \bigg] {}^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { { : \implies}\bf A = 4096 \bigg[1 + \frac{1}{16} \bigg] {}^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { { : \implies}\bf \: A = 4096 \bigg[ \frac{17}{16} \bigg] {}^{3} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { { : \implies}\bf \: A = 4096 \times \frac{17}{16} \times \frac{17}{16} \times \frac{17}{16} } \: \: \: \\ \\ \\ { { : \implies}\bf \: A = 17 \times 17 \times 17} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ { : \implies} {\tt{ \underline{ \boxed{ \pmb{ \frak{A =R s.4913}}}}} \star} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

• So, the amount is Rupees 4913 when compounded half yearly

Hence:

• Ram receives rupees 4,913 respectively

More to know:

• Formula to find amount when compounded annually

${{ : \implies} \bigg[ \bf \: A = P \bigg(1 + \frac{r}{100} \bigg) {}^{n} \bigg]}$

• Formula to find amount when compounded quarterly

${ { : \implies}\bigg[ \bf \: A = P \bigg(1 + \frac{r}{400} \bigg) {}^{3n} \bigg]}$

• Formula to amount interest at different rate of interests compounded

${ { : \implies}\bf \: A = P \bigg[1 + \frac{ r_{1}}{100} \bigg] \bigg[1 + \frac{ r_{2}}{100} \bigg]\bigg[1 + \frac{ r_{3}}{100} \bigg] }$