You want to have $2.5 million in real dollars in an account when you retire in 50 years. The nominal return on your investment is 14 percent and the inflation rate is 3 percent. What real amount must you deposit each year to achieve your goal

The real amount must you deposit each year to achieve your goal is $1,682.0610

Explanation:

In order to calculate the real amount must you deposit each year to achieve your goal first we have to calculate the real rate as follows:

Real rate = (1+nominal rate) / (1+inflation rate) - 1

= (1+0.14) / (1+0.03) - 1

= (1.14/1.03) - 1

0.10679611 (Approx)

So, the real amount must you deposit each year to achieve your goal is calculated by the following formula:

Future value of annuity=Annuity[ (1+rate) ^time period-1]/rate

$2,500,000=Annuity[ (1 + 0.10679611) ^50-1] / 0.10679611

$2,500,000=Annuity*1,486.27188043

Annuity=$2,500,000/1,486.27188043

Annuity=$1,682.0610 (Approx).

The real amount must you deposit each year to achieve your goal is $1,682.0610