Question

Suppose you want to retire when you reach age 70, at that time you want to have $1,000,000 accumulated in your retirement account. Now your 25 years old, starting today, how much you have to save equally, at the beginning of each year, in order to reach your retirement goal if the account earns 5% annually compounded interest?

Answer 1

Future Value of an Annuity Due (Beginning of the month payment)

Future Value = $1,000,000

Annual interest rate (r) = 5.00% per year

Number of years (n) = 45 Years [70 Years – 25 Years]

Annual Payment (P) = ?

Therefore, Future Value of an Annuity Due = (1 + r) x P x [{(1+ r)ⁿ - 1} / r ]

$1,000,000 = (1 + 0.05) x P x [{(1 + 0.05)⁴⁵ - 1} / 0.05]

$1,000,000 = 1.05 x P x [(8.985007793 – 1) / 0.05]

$1,000,000 = 1.05 x P x [(7.985007793 / 0.05]

$1,000,000 = 1.05 x P x 159.7001559

$1,000,000 = P x 167.6851637

P = $1,000,000 / 167.6851637

P = $5,963.56 per year

Hence, the annual savings will be $5,963.56