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
- A18101.76
- B12800
- C9050.88
- 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