Hannah wants to have $ 7500 to help pay for a new deck in 13 years. If she wants to put her money into an account earning 7% interest compounded continuously, how much should she invest now, so that she will have $ 7500 in 13 years?

$ 3,018.93

Step-by-step explanation:

This question is asking us to find the Principal.

Hence, the formula for compound interest that is compounded continuously is :

A = Pe^rt

P = Principal/Initial amount

A = Amount after investment = $7500

r = Interest rate = 7% = 0.07

t = time in years = 13 years

Hence,

7500 = Pe^0.07 × 13

P = 7500/e^0.07 × 13

P = 7500/e^0.97

P = $3018.9316803

Approximately P (The amount that should be invested ) = $3,018.93

24

step-by-step explanation:

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3