In simple interest, you earn interest payments from the principal only. In compound interest, you reinvest the interest payments and earn interest on interest. This is the equation for finding compound interest:

A = P (1 + r / k) ^{k * n}

Where
A = amount in account at end of the year
P = principal
r = rate (usually, an annual rate)
k = number of compounding times per year
n = number of years

John deposited $1,000 at a 10% interest rate for 5 years. How much more money will John have in his account from compound interest than from simple interest if it is compounded semiannually?

Simple Interest:
A = P + (P ´  r ´ t)
A = 1,000 + (1,000 ´ 0.1 ´ 5)
A = 1,000 + (100 ´ 5)
A = 1,000 + 500
A = $1,500

Compound Interest:
A = P (1 + r / k) ^{k * n}
A = 1,000 (1 + 0.1/2) ^{2 * 5}
A = 1,000 (1 + 0.05) ¹⁰
A = 1,000 (1.05) ¹⁰
A = 1,000 ´ 1.62889
A = $1,628.89

$1,628.89 (compound interest) - $1,500 (simple interest) = $128.89

Thus, John will make $128.89 more from compound interest than from simple interest.

Sue received $5,000 from her grandparents on the day she was born. If her parents put the money in First Central Bank, what is the difference in the amount that would be in an account earning simple interest and in an account compounded monthly for the last 10 years? (assume both accounts averaged 6% annual interest)

Estimate the answer:

Less than $500
Between $500 and $1,000
Over $1,000