Answer:
Annually: Future Value ≈ $133.82, Interest Earned ≈ $33.82
Semiannually: Future Value ≈ $134.93, Interest Earned ≈ $34.93
Quarterly: Future Value ≈ $135.42, Interest Earned ≈ $35.42
Monthly: Future Value ≈ $135.80, Interest Earned ≈ $35.80
Daily using Bankers' Rule: Future Value ≈ $136.05, Interest Earned ≈ $36.05
Explanation:
Future Value (FV) = P * (1 + r/n)^(n*t)
Where:
P = Principal amount (initial deposit) = $100
r = Annual interest rate = 6% = 0.06 (decimal)
n = Number of times interest is compounded per year
t = Number of years
Let's calculate the future value and interest earned for each frequency:
Annually (n = 1):
FV = 100 * (1 + 0.06/1)^(1*6)
FV = 100 * (1.06)^6
FV ≈ $133.82
Interest Earned = FV - P
Interest Earned ≈ $133.82 - $100
Interest Earned ≈ $33.82
Semiannually (n = 2):
FV = 100 * (1 + 0.06/2)^(2*6)
FV = 100 * (1.03)^12
FV ≈ $134.93
Interest Earned = FV - P
Interest Earned ≈ $134.93 - $100
Interest Earned ≈ $34.93
Quarterly (n = 4):
FV = 100 * (1 + 0.06/4)^(4*6)
FV = 100 * (1.015)^24
FV ≈ $135.42
Interest Earned = FV - P
Interest Earned ≈ $135.42 - $100
Interest Earned ≈ $35.42
Monthly (n = 12):
FV = 100 * (1 + 0.06/12)^(12*6)
FV = 100 * (1.005)^72
FV ≈ $135.80
Interest Earned = FV - P
Interest Earned ≈ $135.80 - $100
Interest Earned ≈ $35.80
Daily using Bankers' Rule (n = 365):
FV = 100 * (1 + 0.06/365)^(365*6)
FV = 100 * (1.00016438356)^2190
FV ≈ $136.05
Interest Earned = FV - P
Interest Earned ≈ $136.05 - $100
Interest Earned ≈ $36.05
So, the future value and interest earned for each compounding frequency are as follows:
Annually: Future Value ≈ $133.82, Interest Earned ≈ $33.82
Semiannually: Future Value ≈ $134.93, Interest Earned ≈ $34.93
Quarterly: Future Value ≈ $135.42, Interest Earned ≈ $35.42
Monthly: Future Value ≈ $135.80, Interest Earned ≈ $35.80
Daily using Bankers' Rule: Future Value ≈ $136.05, Interest Earned ≈ $36.05