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3 years ago

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Use the formula for computing future value using compound interest to determine the value of an account at the end of 6 years if

a principal amount of $6,000 is deposited in an account at an annual interest rate of 6% and the interest is compounded quarterly.

1 answer:

nadezda [96]3 years ago

5 0

Answer: the value of the account at the end of 6 years is is $8577

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,

P = 6000

r = 6% = 6/100 = 0.06

n = 4 because it was compounded 4 times in a year.

t = 6 years

Therefore,.

A = 6000(1+0.06/4)^4 × 6

A = 6000(1+0.015)^24

A = 6000(1.015)^24

A = $8577

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A marine aquarium has a small tank and a large tank, each containing only red and blue fish. In each tank, the ratio of red fish

Anna007 [38]

Answer:

Ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

Step-by-step explanation:

Let the number of red fish and blue fish in the large tank are x and y respectively.

Similarly ratio of red fish and blue fish in the small tank are x' and y' respectively.

Since in each tank ratio of the red fish to blue fish is 333 : 444

That means x : y = 333 : 444

Or $\frac{x}{y}=\frac{333}{444}$

⇒ $\frac{x}{y}=\frac{3}{4}$

⇒ y = $\frac{4x}{3}$ --------(1)

Similarly x' : y' = 333 : 444

⇒ $\frac{x'}{y'}=\frac{333}{444}$

⇒ $\frac{x'}{y'}=\frac{3}{4}$

⇒ x' = $\frac{3y'}{4}$ ------(2)

Ratio of the fish in large tank to the fish in small tank is 464646 : 555

So (x + y) : (x' + y') = 464646 : 555

$\frac{x+y}{x'+y'}=\frac{464646}{555}$

Now we replace the values of x and y' from equation (1) and equation (2)

$\frac{(x+\frac{4x}{3})}{(\frac{3y'}{4}+y')}=\frac{464646}{555}$

$\frac{\frac{7x}{3}}{\frac{7y'}{4}}=\frac{464646}{555}$

$\frac{4}{3}\times \frac{x}{y'}=\frac{464646}{555}$

$\frac{x}{y'}=\frac{3}{4}\times \frac{464646}{555}$

$\frac{x}{y'}=\frac{232323}{370}$

$\frac{y'}{x}=\frac{370}{232323}$

$\frac{y'}{x}=\frac{10}{6279}$

Therefore, ratio of blue fish in the small tank to the red fish in large tank is 10 : 6279

4 0

3 years ago

Solve with cramer's rule x+2y+3z=11, 2x+y+2z=10, 3x+2y+z=9

nalin [4]

Answer:

x = 2 , y = 0 , z = 3

Step-by-step explanation:

Cramer's rule is a rule through which we can find the solution of linear equation.

we have the three linear equations as

x+2y+3z=11

2x+y+2z=10

3x+2y+z=9

AX=B

A: coefficient matrix

X= unknown vectors(x,y,z)

D = values of the linear equation (11 , 10 , 9)

now we find the determinant of the given linear equation

determinant of the matrix will be

A = $\left[\begin{array}{ccc}1&2&3\\2&1&2\\3&2&1\end{array}\right]$ = 1(1-4) - 2(2-6) + 3(4 - 3)

= 1(-3) - 2(-4) + 3(1)

= -3+8+3 = 8

also D $\neq 0$

so the determinant is Non zero we can apply Cramer's rule

we will be replacing the first column of the coefficient matrix A with the values of D

by replacing the first column we will get the value of the variable 'x'

Dx = $\left[\begin{array}{ccc}11&2&3\\10&1&2\\9&2&1\end{array}\right]$ = 11(1-4) -2(10-18) + 3(20-9) = -33+16+33 = 16

x = $\frac{Dx}{D}$ = $\frac{16}{8}$ = 2

similarly

Dy = $\left[\begin{array}{ccc}1&11&3\\2&10&2\\3&9&1\end{array}\right]$ = 1(10-18) -11(2-6) + 3(18 -30) = -8 +44 -36 = 0

y = $\frac{Dy}{D}$ = 0

Dz= $\left[\begin{array}{ccc}1&2&11\\2&1&10\\3&2&9\end{array}\right]$ = 1(9 - 20) -2(18 - 30) + 11(4 -3) = -11 +24 +11 = 24

z = $\frac{Dz}{D}$ = $\frac{24}{8} = 3$

so we have the solution as

x = 2 , y = 0 , z = 3

Therefore the solution for the given linear equations is (2,0,3).

3 0

3 years ago