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Question

Bilbo Baggins wants to save money to meet three objectives.First, he would like to be able to retire 30 years from now withretirement income of $32,000 per month for 25 years, with the firstpayment received 30 years and 1 month from now. Second, he wouldlike to purchase a cabin in Rivendell in 10 years at an estimatedcost of $420,000. Third, after he passes on at the end of the 25years of withdrawals, he would like to leave an inheritance of$1,350,000 to his nephew Frodo. He can afford to save $4,100 permonth for the next 10 years. If he can earn an EAR of 10 percentbefore he retires and an EAR of 7 percent after he retires, howmuch will he have to save each month in years 11 through 30?

Solution

xxx cash xxxxx for xxxx xxxxxxx xxxxx monthly, xxx the xxxxxxxxxxxx xx xxxxx EAr. xxxxx the xxxxxxxxx xxxxx xxxxxxy, we xxxx geteffective xxxxxxy xxxx. xxx way xx do xxxx xx xx find xxx APR xxxxxxx xxxxxxy xxxxxxxxxxx, and xxxx divide xy xx. xx, thepre-retirement xxx is:

EAR = x.xx= (x+(xxx/xx)]^xx-x, APR = 12*(1.10)^1/12-1] = x.xxxx= x.xx%xxx the xxxx-xxxxxxxxxx APR xx:xxx = x.xx=[x+(xxx/xx)]^xx-x, APR = 12*(1.07)1/12-1] = x.xxxx =x.xx%xxxxx we xxxx calculate xxx xxxx xx needs xx retirement. xxxxxxxxx xxxxx xx retirement xx the xx xx xxx monthly xxxxxxxx plusthe xx xx xxx inheritance. xxx pV xx xxxxx xxx cashflows xx:xxx = $xx,xxx*{x-[x/(x+x.xxxx/xx)^xx*(xx)]}/(x.xxxx/xx) =$x,xxx,xxx.xxxx = 1,350,00/[1+(0.0678/12)]^300 = $7,327,034.05

So, xx xxxxxxxxxx xx need:

$4,616,794.32+ $x,xxx,xxx.xx = $xx,xxx,xxx.xxxx xxxx xx saving $x,xxx per xxxxyx xxx xxx next xx years xxxxxxx xxxxxxxxx xxx cabin. xxx value xx xxx xxxxxxx after xx yearswill xx:xxx = $x,xxx*[{[x+(x.xxxx/xx)]^xxx-x}/(x.xxxx/xx)] =$819,441.81

After xx purchases xxx xxxxx, xxx amount xx will xxxx xx:$xxx,xxx.xx- $x,xx,xxx = $xxx,xxx.xxxx still xxx xx yxxxx untill xxxxxxxxxx. When xx xx xxxxy toretire, xxxx amount xxxx xxxx xxxxx to:

FV = $399,441.81*[1+(0.0957/12)]^240 = $x,xxx,xxx.xxxx, xxxx he xx ready xx xxxxxx, xxxxx on xxx current xxxxxxx, xxxxx xx short:

$11,943,828.37-$2,687,244.78 = $9,256,583.59

This xxxxxx xx xxx Fv xx the xxxxxxy xxxxxxx xx must xxxxxxxxxxx 10 xxx xx . So, xxxxxxx annuity xxyxxxx xxxxx xxx FVAequation, xx find xxx xxxxxxy xxxxxxx will xxxx to xx:xxx = $x,xxx,xxx.xx = x*[{[x+(x.xxxx/xx)]^xxx-x}/(x.xxxx/xx)] =$12,885.82

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