Question

Maria is 40 years old today and she wishes to accumulate $1,840,000 by her sixty-fifth birthday so she can retire to a beach in Florida. She wishes to accumulate this amount by making equal deposits on her fortieth through her sixty-fourth birthdays.

Compute the annual deposit Maria must make if the fund will earn 4% interest compounded annually.

Annual deposit $_______________

Answer 1

Here, the deposits will be same every year, so it is an annuity. And since the deposits will start at the beginning of each year so it will be termed as an annuity due. We will use the following formula of future value of annuity due:

FVAD = (1 + r) * P * ((1 + r)ⁿ - 1 / r)

where, FVAD is future value of annuity due = $1840000, P is the periodical amount, r is the rate of interest = 4% and n is the time period = 25 (65th - 40th birthday)

Now, putting these values in the above formula, we get,

$1840000 = (1 + 4%) * P * ((1 + 4%)²⁵ - 1 / 4%)

$1840000 = (1 + 0.04) * P * ((1 + 0.04)²⁵ - 1 / 0.04)

$1840000 = (1.04) * P * ((1.04)²⁵ - 1 / 0.04)

$1840000 = (1.04) * P * ((2.66583633149 - 1) / 0.04)

$1840000 = (1.04) * P * (1.66583633149 / 0.04)

$1840000 = (1.04) * P * 41.6459082872

$1840000 = 43.3117446187 * P

P = $1840000 / 43.3117446187

P = $42482.70

So, annual deposit = $42482.70