A principal of $5500 is invested in an account paying an annual rate of 5%. Find the amount in the account after 4 years if the account is compounded semi-annually, quarterly, and monthly.

A) Semi Annual; A ≈ $6701.22

B) Quarterly; A = $6709.39

C) Monthly; A = $6715.03

Step-by-step explanation:

We are given;

Principal; P = $5500

Rate; r = 5% = 0.05

Time;t = 4 years

Formula for compound interest is given by;

A = P(1 + r/n)^(nt)

Where n is the number of times the account is compounded per year.

A) In semi annual compounding, it is compounded twice a year, thus n = 2.

A = 5500(1 + 0.05/2)^(2 × 4)

A = 5500(1 + 0.025)^(8)

A = 5500(1.025)^(8)

A ≈ $6701.22

B)In quarterly compounding, it is compounded four times a year, thus n = 4

Thus;

A = 5500(1 + 0.05/4)^(4 × 4)

A = 5500(1 + 0.0125)^(16)

A = 5500(1.0125)^(16)

A = $6709.39

C) In monthly compounding, it is compounded twelve times a year, thus n = 12

Thus;

A = 5500(1 + 0.05/12)^(12 × 4)

A = 5500(1 + 0.004167)^(48)

A = 5500(1.004167)^(48)

A = $6715.03

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.