Sebastian is going to invest in an account paying an interest rate of 1.5% compounded continuously. How much would Sebastian need to invest, to the nearest hundred dollars, for the value of the account to reach $720 in 6 years?

The amount that Sebastian has more than Avery is $1120

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

Considering Sebastian's investment,

P = 32000

r = 2.625% = 2.625/100 = 0.02625

n = 12 because it was compounded 12 times in a year.

t = 18 years

Therefore,.

A = 32000(1 + 0.02625/12)^12 × 18

A = 32000(1+0.0021875)^216

A = 32000(1.0021875)^216

A = 32000 × 1.603

A = 51296

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 32000

r = 2.5% = 2.5/100 = 0.025

t = 18 years

Therefore,

A = 32000 x 2.7183^(0.025 x 18)

A = 32000 x 2.7183^(0.45)

A = 32000 × 1.568

A = 50176

The amount that Sebastian has more than Avery is

51296 - 50176 = $1120

The amount that Sebastian has more than Avery is $1120

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

Considering Sebastian's investment,

P = 32000

r = 2.625% = 2.625/100 = 0.02625

n = 12 because it was compounded 12 times in a year.

t = 18 years

Therefore,.

A = 32000(1 + 0.02625/12)^12 × 18

A = 32000(1+0.0021875)^216

A = 32000(1.0021875)^216

A = 32000 × 1.603

A = 51296

The formula for continuously compounded interest is

A = P x e (r x t)

Where

A represents the future value of the investment after t years.

P represents the present value or initial amount invested

r represents the interest rate

t represents the time in years for which the investment was made.

e is the mathematical constant approximated as 2.7183.

From the information given,

P = 32000

r = 2.5% = 2.5/100 = 0.025

t = 18 years

Therefore,

A = 32000 x 2.7183^(0.025 x 18)

A = 32000 x 2.7183^(0.45)

A = 32000 × 1.568

A = 50176

The amount that Sebastian has more than Avery is

51296 - 50176 = $1120

Given:

Sebastian :

Principal(invested)= $7,100

Rate of interest=  8.14% compounded monthly

Eva:

Principal(invested)= $7,100

Rate of interest= 8.12% compounded continuously

Step-by-step explanation:

After 5 years,

In Sebastian case:

Amount= Principal*

Amount = 7100*

Amount= 7100*

Amount=7100*109.4415

Amount= $777,034.43

In Eva case,

Amount= Principal*

Amount = 7100*

Amount= 7100*130.5818

Amount= $927,130.92

Difference between their money=$927,130.92-777034.43

                                                 =$150,096.49

Eva has $150,096 more money than Sebastian.

Given:

Sebastian :

Principal(invested)= $7,100

Rate of interest=  8.14% compounded monthly

Eva:

Principal(invested)= $7,100

Rate of interest= 8.12% compounded continuously

Step-by-step explanation:

After 5 years,

In Sebastian case:

Amount= Principal*

Amount = 7100*

Amount= 7100*

Amount=7100*109.4415

Amount= $777,034.43

In Eva case,

Amount= Principal*

Amount = 7100*

Amount= 7100*130.5818

Amount= $927,130.92

Difference between their money=$927,130.92-777034.43

                                                 =$150,096.49

Eva has $150,096 more money than Sebastian.

The answer is in the image 

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

For every 8 cars there are 7 trucks

Therefore,

Cars:Truck=8:7

Answer is B)8:7

The solution is in the following image

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

The answer is in the image