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%

i dont understand the question? ?

step-by-step explanation:

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1