P = $25,000 is the principal or present value

t = 10 years

r = annual interest rate

- Continuous Compounding

First lets calculate the compound amount in a continuous compound account

A = P*e^(r*t)

A = 25000 e^(10r)

the interest is A - P = 25000(e^(10r) - 1)

- Compounded Monthly

A = P(1 + i)^n

m = 12 compounding period per year

i = r/m = r/12

n = t*m = 120 total number f compounding periods

A = 25000(1 + r/12)^120

the interest is A - P = 25000((1 + r/12)^120 - 1)

How much more in interest will you earn...?

lets subtract the interests that we have calculated above:

25000(e^(10r) - 1) - 25000((1 + r/12)^120 - 1) =

= 25000((e^(10r) - 1 - (1 + r/12)^120 + 1)=

= 25000(e^(10r) - (1 + r/12)^120)