Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2724958 • 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 do this using a financial calculator.
Explanation / Answer
1 Corpus for returement annuity: PV after 30 Years =A[(1+k)^n-1]/k(1+k)^n EAR =7% pa=0.5833% per month A =26000 per month n=25 years =300 months So PV of fund after 30 years=[26000*(1.005833^300-1)]/0.005833*1.005833^300 PV =3,678,792 So Required fund for annuity after 30 years =3,678,792 2 Inherietence to be left afte 55 years = 1,600,000 PV of inheritence after 30 years =1600000/1.07^25= 1,140,778 So PV of inheritence after 30 years =1,140,778 Total corpus required after 30 years = 4,819,570 3 cost of cabin in 10 years = 360,000 Savings FV of Annuity FV=A(1+k^n-1)/k A =2900 per month k= 10% pa =0.8333% per month n =10 years =120 months FV of Savings after 10 years =2900*(1.008333^120-1)/0.008333 =$594,015 So Amount left after cabin purchase =594015-360000= 234,015 Maturity value of 234015 invested for 20 years @10%=234015*1.10^20= 1,574,336 Total corpus required after 30 years = 4,819,570 Available till now 1,574,336 Remaining fund required = 3,245,234 Assume monthly deposit required A for 20 years so FV =3245234 k= 0.8333% per month n=20 years =240 months so 3245234=A(1.008333^240-1)/0.008333 A =4,273.82 So monthly deposit required =$4,273.82 So the needed saving from yr 11 to 30 is $4,273.82 per month
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