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You deposit $100 in an account earning 6% coumpound interest for 6 years. Find the future value and the interest earned for each of the following compounding frequencies. Use the Bankers' Rule for daily compounding.

SOLVE FOR FUTURE VALUE AS WELL AS INTEREST EARNED

Frequency Future Value Interest Earned

Annually:
Semiannually:
Quarterly:
Monthly:
Daily:

1 Answer

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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

User Ed Haber
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