Suppose that interest on money in the bank accumulates at an annual rate of5% per year compounded continuously. How much money should be invested today, so that 20 years from now it will be worth $20000?
(see attachment)

(Hint: If you're stuck, then model the account balance B = B(t) with a differential equation and an initial condition, keeping in mind that the initial condition here is not at t = 0.)

Question

Suppose that interest on money in the bank accumulates at an annual rate of5% per year compounded continuously. How much money should be invested today, so that 20 years from now it will be worth $20000?
(see attachment)

(Hint: If you're stuck, then model the account balance B = B(t) with a differential equation and an initial condition, keeping in mind that the initial condition here is not at t = 0.)

anonymous · Answer

attachment

anonymous · Answer

7537.79

anonymous · Answer

i'm watching.

anonymous · Answer

P=money invested
R=rate of interest
t=time

anonymous · Answer

?

anonymous · Answer

There are two answers that are close: C and D. If we round then i'm going to assume it's C.

anonymous · Answer

@needhlp my answer above is wrong as it is compunded continously not annually....

anonymous · Answer

$$amount=principal \times (\exp ^{rate timestime})$$

anonymous · Answer

use this equation...
answer =7357.59
so option D

anonymous · Answer

$$20000=principal \times(\exp ^{0.05\times20})$$

anonymous · Answer

i'm going to test it.

anonymous · Answer

it's D! thanks!