Calculating the Future Value of an Ordinary Annuity
The problem involves finding the future value of a series of annuity payments (retirement savings account contributions) made at the end of each year for 30 years, with an annual interest rate of 5.4% (APR). This type of annuity is called an ordinary annuity.
The formula for the future value of an ordinary annuity is:
FV = Pmt × [(1 + r)^n - 1] / r
where:
FV = future value of the annuity
Pmt = annual payment (or contribution)
r = annual interest rate (as a decimal)
n = number of payments (or periods)
Let's plug in the values:
Pmt = $1,200
r = 5.4% or 0.054
n = 30
FV = $1,200 × [(1 + 0.054)^30 - 1] / 0.054
We first calculate (1 + 0.054)^30 and then subtract 1, and finally divide by 0.054 and multiply by $1,200.
Let's do the calculation:
(1 + 0.054)^30 = 4.38903162 (approximately)
4.38903162 - 1 = 3.38903162
3.38903162 / 0.054 = 62.7591075
$1,200 × 62.7591075 = $75,310.929 (approximately)
The future value of the retirement savings account after 30 years when the annual contribution is $1,200 is approximately $75,310.93, when rounded to the nearest cent.
