Question

You plan to work for 40 years and then retire using a 25-year annuity. You want to arrange a retirement income of $4700 per month. You have access to an account that pays an APR of 8.4% compounded monthly.

What size nest egg do you need to achieve the desired monthly yield? (Round your answer to the nearest cent.)

Answer 1

Solution:
	The size nest egg do you need to achieve the desired monthly yield =$588,604.10
Working Notes:
	Since, after 40 years , planning to get $4700 per month for next 25 years , and the size of fund Should to achieve this will be the present value of annuity that is the all expected payment in next 25 years present value on start of retirement
	present value of annuity = Px[ 1-1 /(1 + i)^n)]/ i
	P=monthly payment = $4,700
	i= interest rate per period = 8.4%/12
	n= no. Of period = 12 x 25 =300
	PV of annuity= size nest egg (the fund size required at end of 40thYear)
	present value of annuity = Px[ 1-1 /(1 + i)^n)]/ i
	= 4700 x (1-1/(1+(8.4%/12))^300)/(8.4%/12)
	=$588,604.104031
	=$588,604.10
Please feel free to ask if anything about above solution in comment section of the question.