Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2709819 • 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 $28,500 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 $385,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,725,000 to his nephew Frodo. He can afford to save $3,400 per month for the next 10 years. If he can earn an EAR of 11 percent before he retires and an EAR of 8 percent after he retires, how much will he have to save each month in years 11 through 30?
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 $28,500 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 $385,000. Third, after he passes on at the end of the 25 years of withdrawals, he would like to leave an inheritance of $1,725,000 to his nephew Frodo. He can afford to save $3,400 per month for the next 10 years. If he can earn an EAR of 11 percent before he retires and an EAR of 8 percent after he retires, how much will he have to save each month in years 11 through 30?
Explanation / Answer
Monthly rate prior to retire = (1+11%)^(1/12)-1
Monthly rate prior to retire = 0.8734594%
Monthly rate after retire = (1+8%)^(1/12)-1
Monthly rate after retire = 0.643403%
Amount availablle in account after 10 year = Monthly deposit*((1+r)^n-1)/r - Withdrawl for Estimated cost of car
Amount availablle in account after 10 year = 3400*((1+0.8734594%)^(10*12) -1)/0.8734594% - 385000
Amount availablle in account after 10 year = $ 331,007.12
Amount needed at the time of retirement = monthly withdrawl*(1-(1+r)^-n)/r + Inheritance required *(1+r)^-n
Amount needed at the time of retirement = 28500*(1-(1+ 0.643403%)^-(25*12))/ 0.643403% + 1725000*(1+ 0.643403%)^-(25*12)
Amount needed at the time of retirement = $ 4,034,656.16
Amount accumulated of saving till 10 year = 331,007.12*(1+11%)^20
Amount accumulated of saving till 10 year = $ 2,668,682.52
Remianing Balance Amount needed at the time of retirement = Total Amount needed at the time of retirement - Amount accumulated of saving till 10 year
Remianing Balance Amount needed at the time of retirement = 4,034,656.16-2,668,682.52
Remianing Balance Amount needed at the time of retirement = $ 1,365,973.64
Monthly deposit in years 11 through 30 =Remianing Balance Amount needed at the time of retirement /((1+r)^n-1)/r
Monthly deposit in years 11 through 30 = 1,365,973.64/(((1+0.8734594%)^(20*12) -1)/0.8734594%)
Monthly deposit in years 11 through 30 = $ 1689.42
Answer
Monthly deposit in years 11 through 30 = $ 1689.42
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