Please Help Me Figure This Out

Question

What is the effective annual yield if a deposit of $1000 grows to $4500 in 18 years? Round your answer to two decimal places.

Effective annual yield= % per year

Answer 1

I used the formula i gave you previously and ended-up with this int: .087155= 8.7155%

Answer 2

Hypothetically, if the effective annual yield were 5% (= 0.05) then after one year

an investment of $1000 would become $1000 x 1.05 = $1050.

In general, if the effective annual yield is p, then after a year, the initial investment gets multiplied by (1 + p).

And if you keep the increased investment there, the compounding repeats, and

after n years the multiplicative factor is (1 + p)ⁿ.

In your example, n = 18, so the multiplicative factor after 18 years is (1 + p)¹⁸,

where p is the unknown annual yield.

You know that this multiplicative factor is 4.5, because $1000 became $4500.

So you have to solve the equation

(1 + p)¹⁸ = 4.5

18 x log(1 + p) = log(4.5)

log(1 + p) = 0.036289584

1 + p = 1.08715

p = 8.715%