If an initial investment of $2,400 grows to $31,000 in 18 years, what annual interest rate (as a %) compounded annually did this investment earn? (Round your answer to two decimal places.)

Answer 1

31000 = 2400 (1 + r)¹⁸

12.9167 = (1 + r)¹⁸

ln 12.9167 = 18 ln (1 + r)

2.5585 = 18 ln (1 + r)

0.0078967 = ln (1 + r)

1.081 = 1 + r

0.081 = r

Answer 2

This is Financial Math.

A = final value = 31,000

P = initial value, the principal = 2,400

t = time = 18 years

r = annual rate as a decimal (you will have to multiply it by 100 to get it as percent)

A = P (1 + r)^t

31000 = 2400 (1+r)¹⁸

Solve the equation by dividing both sides by 2400 and then raising both sides to power 1/18.

Multiply the resulting r by 100 to covert it from a decimal to a percent.