Your $6100 investment grows to $12200 over the course of 9 years compounded quarterly. what interest rate did you receive on your investment? (write your answer with at least four decimal points)

The formula is
A=p (1+r/k)^kt
A future value 12200
P present value 6100
R interest rate ?
K compounded quarterly 4
T time 9 years

Set the equation and solve for r (interest rate)
12200=6100 (1+r/4)^(4×9)
Divide both sides by 6100
12200/6100=(1+r/4)^(36)
2=(1+r/4)^(36)
Take the root of 36 for both sides
2^(1/36)=1+r/4
R= (2^(1/36)-1)×4
R=(2^(1÷36)−1)×4
R=0.0778×100
R=7.78%

Hope it helps!