Question

Compound Interest: You deposit $100 in an account that earns 3% annual interest compounded continuously. How long does it take the balance to reach the following amounts? (A = Pe^(rt). NO LINKS

a. $110
b. $150
c. $200

Answer 1

9514 1404 393

Answer:

a) 3.18 years

b) 13.52 years

c) 23.10 years

Explanation:

Solving for t, we find ...

A = Pe^(rt)

A/P = e^(rt)

ln(A/P) = rt

t = ln(A/P)/r

For P=100 and r=.03, the times are ...

a. $110: t = ln(110/100)/.03 ≈ 3.18 years

b. $150: t = ln(150/100)/.03 ≈ 13.52 years

c. $200: t = ln(200/100)/.03 ≈ 23.10 years