Question

Mr. Gulati has a Recurring Deposit Account of
*300 per month. If the rate of interest is 12%
and the maturity value of this account is
8,100; find the time (in years) of this
Recurring Deposit Account.​

Answer 1

The time of Recurring Deposit Account is 2 years  .

Step-by-step explanation:

Given as :

The installment deposited in account per month = p = Rs 300

The rate of interest applied = r = 12%

The maturity value after n years = Amount = A = Rs 8100

Let The time period of maturity = n months

According to question

Standing Instruction = S.I = per month installment × $\dfrac{Rate}{100}$ × $\dfrac{n(n+1)}{2\times 12}$

or,  S.I = Rs 300 × $\dfrac{12}{100}$ × $\dfrac{n(n+1)}{2\times 12}$

or, S.I = Rs $\dfrac{3}{2}$ n ( n + 1 )

Again

Maturity value = S.I + installment amount × number of months

Or,  Rs 8100 = Rs 1.5 n ( n + 1 ) + Rs 300 × n

Or, 8100 = 1.5 ( n² + n ) + 300 n

or,  $\dfrac{8100}{1.5}$ =  ( n² + n ) + $\dfrac{300 n}{1.5}$

Or, 5400 =  ( n² + n ) + 200 n

Or,  ( n² + n ) + 200 n - 5400 = 0

Or,   n² + 201 n - 5400 = 0

Or,  n² + 225 n - 24 n - 5400 = 0

Or, n ( n + 225 ) - 24 ( n +225 ) = 0

Or, ( n +225 ) ( n - 24 ) = 0

i.e  ( n +225 ) = 0    ,   ( n - 24 ) = 0

∴    n = - 225          ,  n = 24

So, The time period of maturity = n = 24 months  = 2 years

Hence, The time of Recurring Deposit Account is 2 years  . Answer

Answer 2

Answer:

Answer is 2years

Step-by-step explanation:

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