Question

You deposit $1000 in a savings account that earns 5% annual interest compounded yearly.

a. Write an exponential equation to determine when the balance of the account will be $1500
b. Solve the equation.

Answer 1

a. 1500 = 1000 × 1.05^x

b. 1500 = 1000 × 1.05^x

Divide both sides by 1000

1500/1000 = 1.05^x

Take the natural log of both sides

ln(1500/1000) = ln(1.05^x)

ln(1.5) = x ln(1.05)

x = ln(1.5) / ln(1.05)

x = 5.12 years