Instructions

1

Suppose the nominal interest rate is 3 percent, and it's not compounded (i.e. it's simple interest). Then a balance of $100 after 2 years is $100x(1+0.03x2) = $106. In other words, the general form for simple interest is 1+it, where i is the interest and t is the amount of time that interest is earned.
2

Suppose the nominal interest rate is 3 percent, compounded annually. Then the above equation becomes (1+i)^t, where the caret ^ indicates exponentiation.

For example, a nominal rate of 3 percent compounded annually for two years turns $100 into $100x(1.03)^2 = $103.19.
3

Suppose the nominal rate is 3 percent, compounded monthly. Then the monthly rate is found from the nominal rate by dividing by 12. This is because the nominal interest rate is, by definition, the periodic interest rate times the number of periods per year.

For example, a nominal rate of 3 percent compounded monthly for two years would turn $100 into $100x(1+0.03/12)^[12*2] = $106.18. In other words, the underlying formula is (1+i/n)^tn, where n is the number of compounding periods in a year, i is the nominal rate, and t is the number of years of compounding.
4

Suppose the nominal interest rate is 3 percent and compounding is continuous. It can be shown that the underlying interest formula is e^it, where i is the nominal rate and t is the number of years. e is "Euler's number," an irrational number approximately equal to 2.71828.

For example, $100 becomes $100xe^[0.03x2] = $106.18 after two years.