Question

Mohan deposited Rs.100 in the bank. Recurring deposit account opened for 5 years per month. If the rate of interest is 5% per annum, what amount will he get after five years?
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Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

Amounts deposited in bank every month, P = Rs 100

Rate of interest, r = 5 % per annum

Time period = 5 years

So,

Number of instâllments, n = 12 × 5 = 60

We know,

Maturity Value (MV) received on a certain sum of money of Rs P deposited every month at the rate of r % per annum for n months is given by

$\bold{{\boxed{\text{MV} = \text{nP} + \text{P} \times \dfrac{ \text{n(n + 1)}}{24} \times \dfrac{ \text{r}}{100} }}}$

So, on substituting the values of n, P and r, we get

$\rm \: \text{MV} = {60 \times 100} + 100 \times \dfrac{ 60(60 + 1)}{24} \times \dfrac{{5}}{100}$

$\rm \: \text{MV} = 6000 + \dfrac{ 5(60 + 1)}{2} \times 5$

$\rm \: \text{MV} = 6000 + \dfrac{ 25 \times 61}{2}$

$\rm \: \text{MV} = 6000 +762.50$

$\rm\implies \:\boxed{ \bf{ \:MV \: = \: Rs \: 6762.50 \: \: }}$

So, Manoj will get Rs 6762.50 on the maturity after 5 years.

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Additional Information :-

Interest (l) received on a certain sum of money of Rs P deposited every month at the rate of r % per annum for n months is given by

$\red{\bold{{\boxed{\text{l} = \text{P} \times \dfrac{ \text{n(n + 1)}}{24} \times \dfrac{ \text{r}}{100} }}} }$

Answer 2

$\; {\underline{\underline{\pmb{\purple{\sf{ \; Given \; :- }}}}}}$

• Money Deposited = Rs.100
• Time = 5 years
• Deposited = per Month
• Rate = 5 %

$\; {\underline{\underline{\pmb{\orange{\sf{ \; To \; Find \; :- }}}}}}$

• Amount Received = ?

$\\ \qquad{\rule{200pt}{2pt}}$

$\; {\underline{\underline{\pmb{\color{darkblue}{\sf{ \; SolutioN \; :- }}}}}}$

$\dag \; {\underline{\underline{\pmb{\sf{ Formula \; Used \; :- }}}}}$

• ${\underline{\boxed{\pmb{\sf{ A = nP + P \times \bigg\lgroup \dfrac{ n ( n + 1) }{24 } \bigg\rgroup \times \dfrac{r}{100} }}}}}$

Where :

• A = Amount
• n = Time
• P = Principal
• r = Rate

$\dag \; {\underline{\underline{\pmb{\sf{ Calculating \; the \; Amount \; :- }}}}}$

$\begin{gathered} \qquad \; \blue\dashrightarrow \; \; \red{\pmb{\sf { A = nP + P \times \bigg\lgroup \dfrac{ n ( n + 1) }{24 } \bigg\rgroup \times \dfrac{r}{100} }}} \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = \bigg( 60 \times 100 \bigg) + 100 \times \bigg\lgroup \dfrac{ 60 ( 60 + 1) }{24 } \bigg\rgroup \times \dfrac{5}{100} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = \bigg( 60 \times 100 \bigg) + 100 \times \bigg\lgroup \dfrac{ \cancel{60} ( 60 + 1) }{ \cancel{24} } \bigg\rgroup \times \dfrac{5}{100} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + 100 \times \bigg\lgroup \dfrac{ 5 ( 60 + 1) }{2} \bigg\rgroup \times \dfrac{5}{100} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + \cancel{100} \times \bigg\lgroup \dfrac{ 5 ( 60 + 1) }{2 } \bigg\rgroup \times \dfrac{5}{ \cancel{100} } } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + \bigg\lgroup \dfrac{ 5 ( 60 + 1) }{2 } \bigg\rgroup \times 5 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + \bigg\lgroup \dfrac{ 5 \times 61 }{2 } \bigg\rgroup \times 5 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + \dfrac{ 305 }{2 } \times \dfrac{5}{1} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + \cancel\dfrac{ 305 }{2} \times \dfrac{5}{1} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; \sf { A = 6000 + 762.5 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \dashrightarrow \; \; {\underline{\boxed{\pmb{\frak{ Amount = Rs. \; 6762.5 }}}}} \; \purple\bigstar \\ \\ \\ \end{gathered}$

$\therefore \;$ Mohan will get Rs.6762.5 .

$\\ \qquad{\rule{200pt}{2pt}}$