Question - Calculating the Future Value of an Ordinary Annuity
Solution:
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] / rwhere:FV = future value of the annuityPmt = annual payment (or contribution)r = annual interest rate (as a decimal)n = number of payments (or periods)Let's plug in the values:Pmt = $1,200r = 5.4% or 0.054n = 30FV = $1,200 × [(1 + 0.054)^30 - 1] / 0.054We 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 = 3.389031623.38903162 / 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.
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com