How long will it take so the balance will reach $2500.

Question

Assume you have deposited $1500 into a bank with a fixed interest rate of 5% a and compounded continuously. How long will it take so the balance will reach $2500. Please show work. 

Answer 1

Let A(t) = amount in the account after t years.  Since interest is compounded continuously, A(t) = Pe^rt, where P is the initial investment amount and r is the interest rate expressed in decimal form.

 

So, in this problem, A(t) = 1500e^0.05t.

 

The balance reaches 2500 when A(t) = 2500.

 

We have: 2500 = 1500e^0.05t

 

Divide by 1500 to get 5/3 = e^0.05t.

 

Take natural log of both sides to obtain ln(5/3) = lne^0.05t.

 

Since lne^x = x, ln(5/3) = 0.05t

 

So, t = ln(5/3)/(0.05) ≈ 10.2 years.