Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2724974 • Letter: B
Question
Bilbo Baggins wants to save money to meet three objectives. First, he would like to be able to retire 30 years from now with retirement income of $26,000 per month for 25 years, with the first payment received 30 years and 1 month from now. Second, he would like to purchase a cabin in Rivendell in 10 years at an estimated cost of $360,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,600,000 to his nephew Frodo. He can afford to save $2,900 per month for the next 10 years. If he can earn an EAR of 10 percent before he retires and an EAR of 7 percent after he retires, how much will he have to save each month in years 11 through 30? Please help me understand this by using a financial calculator.
Explanation / Answer
Answer: EAR =(1+APR/m)^m-1
APR for working period is 9.57%
APR for retirement period is 6.78%
Value at beginning of retirement of the $1,600,000 inheritance
Value at beginning of retirement of the 25 years of monthly receipts of $26,000
Present value=Present value of Annuity+PV of Inheritence
=$26000*PVIFA+1600,000*PVIF
=$26000*[1-(1/(1+0.0678/12)^300)/0.0678/12]+$1600,000/(1+0.0678/12)^300
=$3750552.62+$295163.465
=$4045716.09
Future value=FV of Annuity
=$2900*((1+0.0957/12)^120-1)/(0.0957/12)
FV=579605.18
Bilbo has saved $579605.18
He pays $360,000 for the house
That means that he has $219605.18 left in his bank account.
Future value=$219605.18*(1+0.797)^240
=1477393.85
Bilbo will have $1477393.85
Bilbo needs $4045716.09
There Bilbo needs to save $4045716.09- $1477393.85
•Needed savings if $2568322.2
Future value of Annuity=PMT*FVIFA
$2568322.24=PMT*{(1+0.0957/12)^240 -1/0.0957/12}
PMT=$3575.76
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