Question

Renu has cumulative deposit account of rupees 200 per month at 10% per annum if she gets Rupees 6775 at the time of maturity find the total time for which the account was held

Answer 1

Given :

The money deposit = Rs 200 per month

The rate of interest = 10%

The maturity amount = Rs 6775

To Find :

The time period

Solution :

The interest on this value = I

Or, I = $\dfrac{n(n+1)}{2}$ × $\dfrac{installment \times rate}{12\times 100}$

or,  I =  $\dfrac{n(n+1)}{2}$ × $\dfrac{200 \times 10}{1200}$

Or, Interest = $\dfrac{n(n+1)}{2}$ × $\dfrac{5}{3}$

Now,

Maturity  value = installment × rate + Interest

Or,  Rs 6775 = 200 × 10 + $\dfrac{n(n+1)}{2}$ × $\dfrac{5}{3}$

Or, 6775 - 2000 = $\dfrac{n(n+1)}{2}$ × $\dfrac{5}{3}$

Or, 4775 = $\dfrac{n(n+1)}{2}$ × $\dfrac{5}{3}$

Or, $\dfrac{n(n+1)}{2}$ = $\dfrac{955}{3}$

Or,  n ( n + 1 ) = $\dfrac{1910}{3}$

Or,  n ( n + 1 ) = 636.67

∴   n² + n - 636.37 = 0

Solving this quadratic equation

n =     $\dfrac{-1\pm \sqrt{(-1)^{2}-4\times 1\times (-636.37)}}{2\times 1}$                                                                                                                    

n = 24 . 7   ,  -  25 .7

i.e  n = 25 , - 26

So, we consider n = 25

Or,  number of month = 25

Hence The number of month for which account held is 25 . Answer