SOLUTION: when interest is compounded continouously, the balance in an account after t years is given by P(t)= P(0)*e^kt, where P0 is the initial investment and k is the interest rate. suppo

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: when interest is compounded continouously, the balance in an account after t years is given by P(t)= P(0)*e^kt, where P0 is the initial investment and k is the interest rate. suppo      Log On


   

Question 285747: when interest is compounded continouously, the balance in an account after t years is given by P(t)= P(0)*e^kt, where P0 is the initial investment and k is the interest rate. suppose that p(0) is invested in a savings account where interest is compounded at 1% per year. Express P(t) in terms of P(0) and 0.01
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
Continuous Compounding Formula is:

P(t) = P(0) * e^(k*t) where:

P(t) = Future Value
P(0) = Present Amount
k = Annual Interest Rate
t = Number of Years

Discrete Compounding Formula is:

P(t) = P(0) * (1+(k/c)^(t*c) where:

P(t) = Future Value
P(0) = Present Amount
k = Annual Interest Rate
t = Number of years
c = Compounding periods per Year.

If the annual interest rate is 1%/100% = .01, and if the compounding periods per year are equal to 1 (annual compounding), then:

Your continuous compounding formula would be:

P(t) = P(0) * e^(.01*t)

Your discrete compounding formula would be

P(t) = P(0) * (1.01)^t