Question

What will be the value of an investment if you put $2,000 at the end of each year into a retirement plan yielding 7% annually for 25 years (ordinary annuity)? What is the future value if the payment is deposited at the beginning of each year ((annuity due)?

Answer 1

The Future Value if the payments are made at the end of each year (ordinary annuity)

Annual Payments = $2,000 per year

Interest Rate (r) = 7%

Number of Years = 25 Years

Future Value of Ordinary Annuity = P x [{(1+ r) ⁿ - 1} / r ]

= $2,000 x [{(1 + 0.07)²⁵ – 1} / 0.07]

= $2,000 x [(5.42743 – 1) / 0.07]

= $2,000 x [4.42743 / 0.07]

= $2,000 x 63.24904

= $1,26,498.08

“The Future Value = $1,26,498.08”

The Future Value if the payments are made at the beginning og each year (Annuity Due)

Annual Payments = $2,000 per year

Interest Rate (r) = 7%

Number of Years = 25 Years

Future Value of Ordinary Annuity = (1 + r) x P x [{(1+ r) ⁿ - 1} / r ]

= (1 + 0.07) x $2,000 x [{(1 + 0.07)²⁵ – 1} / 0.07]

= 1.07 x $2,000 x [(5.42743 – 1) / 0.07]

= 1.07 x $2,000 x [4.42743 / 0.07]

= 1.07 x $2,000 x 63.24904

= $1,35,352.94

“The Future Value = $1,35,352.94”