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

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