Question

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.

Answer 1

• 5% compounded
• $2495.31

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

__

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.

__

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.