You want to have $6 million in real dollars in an account when you retire in...

You want to have $6 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 5.1 percent.

What real amount must you deposit each year to achieve your goal? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Expert Solution

Solution:
	Real amount must you deposit each year	$26,287.55

Working Notes:
	As per Fisher effect

	(1+ real rate) (1+inflation) = (1+ nominal rate of interest)
	where real rate is constant

	(1+ real rate) (1+inflation) = (1+ nominal rate of interest)
	(1+ real rate) (1+ 5.1%) = (1+ 13%)
	Real rate r = (1.13/1.051) - 1
	Real rate r = 0.075166508


	Future value of annuity = P x ((1+i)^n - 1)/i

	P= deposit each year =??
	Future value of annuity =$6 million at end of 40th years
	i=interest rate = 0.075166508
	n= no. Of years= 40 Year


	Future value of annuity= P x ((1+i)^n - 1)/i
	6,000,000 = P x ((1+0.075166508)^40 - 1)/0.075166508
	6,000,000 = P x 228.2449123
	P= 6,000,000/228.2449123
	P= $26,287.552
	P= $26,287.55

Notes:	Real amount must you deposit each year	$26,287.55

Please feel free to ask if anything about above solution in comment section of the question.

jeff jeffy answered 1 year ago

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