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

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

Amount deposited per month, P = Rs 100

Rate of interest, r = 6 % per annum

Time = 5 years = 5 × 12 = 60 months

Number of instâllments, n= 60

We know,

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

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

So, on substituting the values of n, P and r from above, we have

$\rm \: \text{MV} ={60 \times 100} + {100} \times \dfrac{{60(60 + 1)}}{24} \times \dfrac{ \text{6}}{100}$

$\rm \: \text{MV} ={6000} + 15 \times 61$

$\rm \: \text{MV} ={6000} + 915$

$\rm\implies \:\rm \: \text{MV} = 6915$

So,

Amount received on maturity = Rs 6915

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

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

$\pink{\boxed{\tt{ MV \: = \: \text{P} \: + \: I \: }}}$

Answer 2

Information provided with us :

• 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:-

• $\boxed{\tt{M.V. \: = \: P \times \: n \: + \: I }}$

Interest:-

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

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 :

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

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

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

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

$: \longmapsto \: \tt{I \: = \: \cancel{100} \times \dfrac{3660}{24} \: \times \: \dfrac{6}{ \cancel{100}} }$

$: \longmapsto \: \tt{I \: = \: \dfrac{3660}{24} \: \times \: 6}$

$: \longmapsto \: \tt{I \: = \: \dfrac{3660}{ \cancel{24}} \: \times \: \cancel {6}}$

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

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

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

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

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

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

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

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