Your parents will retire in 30 years. They currently have $350,000 saved, and they think they will need $1,450,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

4.85%

Step-by-step explanation:

1450000 = 350000(x³⁰)

x³⁰ = 4.1428571429

30lgx = lg4.1428571429

lgx = 0.0205766653

x = 10^0.0205766653

x = 1.0485198708

104.85%

So, interest is 4.85%

the interest rate is 4.86%

Step-by-step explanation:

Assuming the interest was compounded annually, 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,

P = $350000

A = $1450000

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

t = 30 years

Therefore,.

1450000 = 350000(1+r/1)^1 × 30

1450000/350000 = (1 + r)^30

4.14 = (1 + r)^30

Taking log of both sides of the equation, it becomes

Log 4.14 = 30 log(1 + r)

0.617 = 30 log (1 + r)

0.0206 = log(1 + r)

Taking exponent of both sides, it becomes

10^0.0206 = 10^log(1 + r)

1 + r = 1.0486

r = 1.0486 - 1 = 0.0486

Converting to percentage, it becomes

r = 0.0486 × 100 = 4.86%

maybe showing the graph would

step-by-step explanation:

-387129 iq

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be