Answer:
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
