Question

You want to have $5 million in real dollars in an account when you retire in 40 years. The nominal return on your investment is 13 percent and the inflation rate is 4.4 percent. 1.) What real amount must you deposit each year to achieve your goal? (Do not round intermediate calculations and round your final answers to 2 decimal places. (e.g., 32.16)) $_______Deposit Amount

Answer 1

Answer: $18,128.27

Explanation:

Real interest rate = [( 1 + Nominal rate ) / ( 1 + inflation rate)] - 1

= [(1 + 13%) / ( 1 + 4.4%) ] - 1

= 8.2375478927203065134%

This is dealing with the future value of an annuity where $5,000,000 is that future value.

Future Value of an annuity = Amount * {[((1 + r )^n) - 1] / r}

5,000,000 = Amount * {[((1 + 8.2375478927203065134%% )^ 40) - 1] / 8.2375478927203065134%}

5,000,000 = Amount * 275.81229325572622843153903061969

Amount = 5,000,000/275.81229325572622843153903061969

= $18,128.27