P = $100,000 million the principal

r1 = 0.05 or 5% annual rate

r2 = 0.055 or 5.5% annual rate

m = 4 compounding period per year (compounded quarterly)

i1 = r1/4 = 0.05/4 interest rate per period

i2 = r2/4 = 0.055/4 interest rate per period

t = 10 years is the time in years

n = t*m = 10*4 = 40 is the total number of compounding periods

A = the future value

The formula for the future value is:

A = P(1 + i)^n

I = the interest earned

I = A - P

I = P((1 + i)^n - 1)

The interest earned at annual interest rate of 5% is: I1 = P((1 + i1)^n - 1)

The interest earned at annual interest rate of 5.5% is: I2 = P((1 + i2)^n - 1)

We need to find I2 - I1:

P((1 + i2)^n - 1) - P((1 + i1)^n - 1) = P((1 + i2)^n - 1 - (1 + i1)^n + 1) = P((1 + i2)^n - (1 + i1)^n)

P((1 + i2)^n - (1 + i1)^n) = 100000((1 + 0.055/4)^40 - (1 + 0.05/4)^40) = $8,315.13

The interest earned at 5.5% annual interest rate is by $8,315.13 bigger then the interest earned at 5% annual interest.