Question

Mohan opened a Recurring deposit Account in a bank for five year and deposite 100 RS every month. If the rate of interest 6% per annum them how much money will he get after 5 years.​​

Answer 1

Answer:

☼︎Information Provided:

• Mohan opened a Recurring deposit Account in a bank for five years

• He deposited Rs.100 every month

• Rate of interest is 6% per annum

☼︎What we have to calculate :

• How much money will he get after 5 years?

☼︎Using Formulas :

☼︎Maturity value:-

$\boxed{\sf{\longmapsto \: M.V. \: = \: P \times \: n \: + \: I }}$

☼︎Interest:-

$\boxed{\sf{\longmapsto \: I\: = \: P \times \: \frac{n(n + 1)}{2 \times 12} \: + \: \dfrac{r}{100} }}$

☼︎In both the formulas,

• P is Principal

• n is number of months

• r is rate of interest

☼︎Performing Calculations :

Finding out the interest by substituting the values in the given formula of calculating the interest~

☼︎Number of months :

☼︎We know that,

• 1 year = 12 months

• 5 years = 12 × 5 months

• 5 years = 60 months

☼︎We have :

• P is 100

• r is 6%

• n is 60

☼︎Putting the values :

$\: \tt { \longmapsto \: I \ \: = \: 100 \times \dfrac{60(60 + 1)}{2 \times 12} \: \times \: \dfrac{6}{100} }$

$\: \sf{I \: = \:100 \times \dfrac{60(61)}{2 \times 12} \: \times \: \dfrac{6}{100} }$

$\: \sf{I \: = \:100 \times \dfrac{60 \times 61}{2 \times 12} \: \times \: \dfrac{6}{100} }$

$\: \sf{I \: = \: 100 \times \dfrac{3660}{24} \: \times \: \dfrac{6}{100} }$

$\: \sf{I \: = \: \dfrac{3660}{ \cancel{24}} \: \times \: \cancel {6}}:⟼I=243660×6$

$: \longmapsto \: \sf{I \: = \: \dfrac{3660}{4}}$

$: \longmapsto \: \sf{I \: = \: \cancel\dfrac{3660}{4}}$

$: \longmapsto \: \boxed{ \mathfrak \green{{I \: = \: 915} }}$

☼︎Now, putting the values in formula of M.V. :

${ \underline {\rule{9cm}{0.3cm}}}$

$... \: \sf{\longmapsto \: M.V. \: = \: 100 \: \times \: 60 + \: 915}$

$... \sf{ \longmapsto\: M.V. \: = \: 6000 + \: 915}:$

$... \longmapsto \: \boxed{\pink{\sf{M.V. \: = \mathfrak {6915}}}}:$

$\underline{\bf{Hence \: he \: would \: get \: Rs.6915 \: after \: 5 \: years}}$

${ \underline {\rule{9cm}{0.3cm}}}$

☼︎Additional Information

Interest (I) received on maturity on the investment of Rs P per month at the rate of r % per annum for n months is

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

Maturity Value (MV)

 Received on maturity on the investment of Rs P per month at the rate of r % per annum for n months is also given by

$\begin{gathered} \pink{\boxed{\rm{ MV \: = \: \text{P} \: + \: I \: }}} \\ \end{gathered}$

${ \underline {\rule{9cm}{0.3cm}}}$