You are given a choice of taking the simple interest on $100,000 invested for 4 years at a rate of 5% or the interest on $100,000 invested for 4 years at an interest rate of 5% compounded daily (use the Bankers rule). Which investment earns a greater amount of interest? Give the difference between the amounts of interest earned by the two investments.

Step-by-step explanation:

The amount (A) resulting from principal P invested at simple interest rate r for t years is ...

  A = P(1 +rt)

  A = $100,000(1 +0.05·4) = $120,000

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The amount resulting from interest being compounded daily is ...

  A = P(1 +r/360)^(365.25t)

  A = $100,000(1.00013888...)^1461 = $122,495.31

The "Banker's rule" says the daily rate is based on 360 days per year. The actual interest is computed based on the exact number of days. In 4 years, there will be a leap year, so that's 1461 days.

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The investment with compounded interest earns more.

  $122,495.31 -120,000.00 = $2,495.31

The difference in interest earned is $2,495.31.

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step-by-step explanation:

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for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis: