Question

How much more interest will Maria receive if she invests $1,000 for one year at x percent annual interest, compounded semiannually, than if she invests $1,000 for one year at x percent annual interest, compounded annually?

Answer 1

Answer:

  $0.025x² . . . where x is a number of percentage points

Step-by-step explanation:

The multiplier for semi-annual compounding will be ...

  (1 + x/2)² = 1 + x + x²/4

The multiplier for annual compounding will be ...

  1 + x

The multiplier for semiannual compounding is greater by ...

  (1 + x + x²/4) - (1 + x) = x²/4

Maria's interest will be greater by $1000×(x²/4) = $250x², where x is a decimal fraction.

If x is a percent value, as in x = 6 when x percent = 6%, then the difference amount is ...

  $250·(x/100)² = $0.025x² . . . where x is a number of percentage points

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Example:

For x percent = 6%, the difference in interest earned on $1000 for one year is $0.025×6² = $0.90.