Multiple choices are:
$321.89
$389.21
$455.93
$492.45
$588.71
$633.33
$722.22
$739.33
$751.33
$321.89 



$389.21 


$455.93 


$492.45 


$588.71 


$633.33 


$722.22 


$739.33 


$751.33 
'
Question
(Finding an annuity payment) suppose you would like to be paid $30,000 per year during your retirement, which starts in 25 years. Assume the 30,000 is an annual perpetuity and the expected return is 6% APY. What should you save per month for the next 25 years so that you can achieve your retirement goal?
Multiple choices are:
$321.89
$389.21
$455.93
$492.45
$588.71
$633.33
$722.22
$739.33
$751.33
$321.89 



$389.21 


$455.93 


$492.45 


$588.71 


$633.33 


$722.22 


$739.33 


$751.33 
Solution
Future value = present value *(1+r)^t, where r is the interest rate, and t is the year Present value of a perpetuity = C/r, where C is the annual payment and r is the interest rate Monthly savings 751.33 We will use r=.06 in both above formulas because the APY (annual percentage yield) is 6% Future value of annual savings = Present value of perpetuity 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Annual savings 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 9016 Future value 36505 34439 32489 30650 28915 27279 25735 24278 22904 21607 20384 19230 18142 17115 16146 15232 14370 13557 12789 12065 11382 10738 10130 9557 9016 Sum of future values 494656 Present value of perpetuity = 30000/.06 500000 To achieve the retirement goal we should save $751.33 Since 751.33 is the closest you get to saving if you want to have around 500,000 in year 25, which is the present value of a perpetuity that pays 30000 every year
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