6. Linda puts \$100 in the bank each month for 15 years. If the bank gives 6% annual interest compounded monthly, how much will she have after 15 years?

This is an annuity problem so you will need to use the annuity formula which is punched into the calculator as

F = R((1 + r/m)mt - 1)/(r/m)

where

R is the periodic deposit or rent

r is the annumal interest rate,

m is the number of times per year that interest is compounded

t is the number of years, and

F is the amount of money in the account after all these deposits. F is also known as the future value.

In this case,

R = 100

r = .06

m = 12

t = 15

This is punched into the calculator as

= 100((1 + .06/12)^(12x15) - 1)/(.06/12)

= \$29,081.87

rounded to the nearest cent.

In this case where the periodic interest rate comes out even after just three places after the decimal, it is perfectly all right to punch in

100(1.005^180 - 1)/.005

but if the periodic interest rate does not terminate in a few places, this annuity formula is very sensitive to round off error in the computation.