Question

Suppose that interest on money in the bank accumulates at an annual rate of 5% per year compounded continuously. How much money should be invested today, so that 20 years from now it will be worth $20,000?
(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)
A. $5498.23
B. $6766.49
C. $7982.22
D. $7357.59
E. $5909.04

Answer 1

I think its answer D but I am not sure.

Answer 2

yea it was that

Answer 3

A e^rt = 20,000
A e^.05*20 = 20,000
ln A + 1 = 9.903
ln A = 8.903
A = 7357.59

Answer 4

p * e^(rt) = 20000

p = 20000 / [e^(.05 * 20)] = 20000 / e