Word problem help

Question

Suppose $5000 is invested at interest rate k, compounded continuously, and grows to $6954.84 in 6 years. Find interest rate. Find exponential rate, find balance after 10 years, find the doubling time?

 

help!!!!

Answer 1

Continuously compounded interest formula:

 

A = Pe^kt

 

In this case we know A = $6954.84, t = 6 years and P = $5000.00.

 

To solve for k

 

ln(A) = ln(P) + kt

 

kt = ln(A) - ln(P)

 

k = [ln(A) -ln(P)]/t = (0.33)/6 years 

 

k = 0.055 or 5.5% per year