Question

To get a maturity value of ₹ 65,592 at the rate of 9% with the monthly instalment of ₹ 1,600, what

should be the time period of the account?​

Answer 1

Given : a maturity value of ₹ 65,592 at the rate of 9% with the monthly instalment of ₹ 1,600

To find : what  should be the time period of the account?​

Solution:

Monthly installments  =  ₹ 1,600

Let say n month is time period

=> Amount invested  = 1600n

interest for amount deposited 1st month  = 1600 * 9 * n/12) /100  =  12n

interest for amount deposited 2nd month  = 1600 * 9 * ((n-1)/12) /100  =  12(n-1)

Total amount  =  1600n + 12n + 12(n-1) +......................12

= 1600n + 12 ( n + (n-1) + ............ + 1)

= 1600n + 12 n(n+1)/2

= 1600 n+  6n² + 6n  

6n² +  1606n   = 65592

=> 6n²  + 1606n  - 65592 = 0

=>3n²  +803n  - 32796 = 0

=> n = 36

time period of the account  = 36  months

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Answer 2

Step-by-step explanation:

Given To get a maturity value of ₹ 65,592 at the rate of 9% with the monthly installment of ₹ 1,600, what should be the time period of the account?

• Monthly installment = Rs 1600
• Rate is 9% and maturity value is Rs 65,592
• Let t be the number of months
• t = t(t + 1) / 2 x 12
• So Amount = pt + PTR / 100
•      65592 = 1600 x t + 1600 x t(t + 1) x 9 / 2 x 12 x 100
•     65592 = 1600 x t + 6t^2 + 6t
•    6t^2 + 1606 t – 65592 = 0

  So we have,

•         t = - b ± √b^2 – 4ac / 2a
•               = - 1606 ± √(1606)^2 – 4(6)(-65592) / 2(6)
•              = - 1606 ± √2579236 + 1574208 / 12
•               = - 1606 ± √4153444 / 12
•               = - 1606 ± 2038 / 12
•              = 2038 – 1606 / 12
•               = 432 / 12
•              = 36
• Or t = 36 months

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