Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202526 Apr 2025Morning ShiftMathematicsDifferential EquationsActual

The money invested in a company is compounded continuously. If ₹ 400 invested today becomes ₹800 in 6 years, then at the end of 30 years, it will become (in ₹)

Options

  1. A18101.76
  2. B12800
  3. C9050.88
  4. D12804

Correct answer

B. 12800

Step-by-step solution

The continuous compounding formula is A = Pe^ rt , where P is the principal and t is time in years. Given P = 400 and A = 800 at t = 6 , we have 800 = 400e^ 6r . Dividing both sides by 400 yields 2 = e^ 6r , and taking natural logarithms gives (2) = 6r . Solving for r : r = (2) 6 . For t = 30 years, A = 400e^ 30r = 400e^ 5 (2) = 400e^ (32) = 400 32 = 12800 . Final amount: ₹12800

Practice Differential Equations on Quantrex Academy →

More from Differential Equations

The general solution of the differential equation (x y x ) d y= (y y x -x ) d x is 2025The general solution of the differential equation (x+y) d y=d x is 2025If Ax ^3+ Bxy =4 (A and B are arbitrary constants) is the general solution of the differential equation F(x) d^2 y d x^2 +G(x) d y d x -2 y=0 , then F(1)+G(1)= 2025If y=A t^2+ B t (A,B are parameters) is general solution of the differential equation f(t) y^ (t)+g(t) y^ (t)+h(t) y=0 then 2 f(t)+t^2 h(t)= 2025The general solution of the differential equation (2 x-y)^2 d y-2(2 x-y)^2 d x-2 d x=0 is 2025The general solution of the differential equation x x d y=(x x-y) d x is 2025If a and b are arbitrary constants, then the differential equation corresponding to the family of curves y= (a x+b) is 2025The general solution of the differential equation x y(y+2) d y+ (y^3-1 ) d x=0 is 2025 Full Differential Equations list All MHT CET PYQs