If you invest in P dollars and you want the investment to grow to A dollars in t years, the interest rate that must be earned if interest is compounded annually is given by the formula
r =t√A/P-1
If you invest $4000 and want to have $8500 in 8 years, what interest rate must be earned? Round to at least 1 decimal place.

You need an interest rate of at least percent.

You need an interest rate of at least 9.9%

Step-by-step explanation:

We would apply the formula for determining compound interest which is expressed as

A = P(1 + r/n)^nt

Where

A = total amount in the account at the end of t years

r represents the interest rate.

n represents the periodic interval at which it was compounded.

P represents the principal or initial amount deposited

From the information given,

A = $8500

P = $4000

n = 1 because it was compounded once in a year.

t = 8 years

Therefore,

8500 = 4000(1 + r/1)^1 × 8

8500/4000 = (1 + r)^8

2.125 = (1 + r)^8

Taking log of both sides of the equation, it becomes

Log 2.125 = 8 log (1 + r)

0.327 = 8 log (1 + r)

0.327/8 = 8 log (1 + r)

0.040875 = log (1 + r)

Taking inverse log of both sides of the equation, it becomes

10^0.040875 = 10^log (1 + r)

1.099 = 1 + r

r = 1.099 - 1

r = 0.099

r = 0.099 × 100 = 9.9%

yep

step-by-step explanation:

check above link.

graphically?   well, you graph them both, the solutions is where they both intersect each other, since there are two solutions, meaning they will meet twice, or namely the linear will run into the quadratic curve twice, and where they meet, those x,y coordinates are the solutions to the system.