Bilbo Baggins wants to save money to meet three objectives. First, he would like
ID: 2723900 • 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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
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? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
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 Savongs 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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