Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.) $250/month for 19 years at 6%/year compounded monthly

Question

Find the amount (future value) of the ordinary annuity. (Round your answer to the nearest cent.)

$250/month for 19 years at 6%/year compounded monthly

= $______

Answer 1

The key to understanding how to use a formula and solving these and any other type of problem is to know what each part of the equation represents. For future value of an ordinary annuity, you have the equation:

FV = C [( 1 + i)ⁿ - 1] / i

FV = future value

C = amount paid each period

r = the annual interest rate (represented as a decimal)

p = # of periods per year

i = r ⁄ p (represented as a decimal)

n = # of periods = [(# of years) * p]

Notice I included two variables that are not in the problem, r and p. These are included because they are "implied" variables required to go from the words in the problem to the formula. If the annual interest rate, r, is used instead of the period interest rate, i, for any compounding period other than annually you will overestimate the future value. Similarly, using the number of years rather than the number of periods may cause you to underestimate the future value.

For the problem above:

C = $250

r = 6% = 0.06

p = 12 (since there are 12 months in a year)

i = 0.06 ⁄ 12 = 0.005

n = 19 + 12 = 228

FV = ($250) [ (1.005)²²⁸ - 1] ⁄ (0.005) = $105,894.96