What is the annual rate of interest for this account?

Question

An initial deposit of 4,000 is made in a savings account for which the interest is compounded continuously. The balance will double in seven years.

Answer 1

There are two approaches to this problem.

Remember that P(t)=P₀e^kt for any form of continuous exponential growth.

Since the money doubled, we know that it is going to be 8000 when t=7.

Solve the equation 8000=4000e^k(7) to find the value of k.

2=e^7k

ln 2=7k

k = 0.099  or 9.9%

 

The other method is to use the doubling time formula: ln 2 = kt

ln2 = 7k

k = 0.099 or 9.9%