Exponential functions

Question

If $535 is invested at an interest rate of 6% per year and is compounded continuously, how much will the investment be worth in 10 years? 

Answer 1

For continuously compounded interest, we use the formula

 

A = Pe^rt

 

where A is the amount of interest after compounding, 

P is the initial amount invested, 

e is the natural exponential function,

r is the rate, and

t is the amount of time the investment has to grow.

 

Plugging in our values, we find that

 

A = ($535)e^(0.06)(10)

 

   = ($535)(1.8221)

 

   = $974.83