Question

Ms. Ieda Silva plans to retire in 28 years and expects to live for 25 years after retirement. She is preparing a savings plan to meet the following objectives. First, after retirement she would like to be able to withdraw $20,000 per month. The first withdrawal will occur at the end of the first month after retirement. Second, she would like to leave her son an inheritance of $500,000 when she passes on. Finally, she would like to set up a fund that will pay $15,000 per month forever to her favorite charity after she passes on. These payments to the charity will start one month after she passes on. All monies can earn 10 percent annual rate compounded monthly. How much will she have to save per month to meet these objectives? She wishes to make the first deposit a month from now and the last deposit on the day she retires.

Answer 1

Rate 10% Compounded monthly, therefore r = 10/12=0.833396 Tenure 25 years Compounded monthly, therefore n = 25 years*12=300 months For 25 years 1 Withdrawal of 20000 per month 2 Sum of 500000 at the end of 25th year 3 Charity of 15000 per month after death, forever Present Value Present value annuity factor for 0.8333% and for 300 months is 110.0472301 at retirement 1 Present value of monthly withdrawal of 20000 for 25 years 20000 110.0472301 2200944.602 2 Sum of 500000 at the end of 25th year 500000* Present value factor at 25th year of 0.83333396 = 500000*0.0829 41470 3 Charity of 15000 per month after death, forever Present value = Monthly payout/Interest rate = 15000/0.8333333% 1800000 Total 4042414.602 Therefore at the end of 28 years that is at the time of retirement, Ms. Leda should have 4042415 To get 4042415 Ms. Leda need to deposit monthly amount at the rate 10% per annum, is calculated by following formula (payment made at the end of the month ) A = PMD[(1+r)^n - 1)]/r Where, A = Future value = 4042415 PMD = Monthly amount need to deposit r = Monthly Interest rate = 0.833333396 n=No. of months = 28 12 = 336 Therefore, 4042415 = PMD [(1.008333) 336-1)]/0.0083333 PMD = 33687 /15.2549 PMD=2208.28 To get 4042415 Ms. Leda need to deposit monthly amount at the rate 10% per annum, is calculated by following formula payment made at the beginning of the month) A = PMD[(1+r)^n - 1)(1+r)]/r Where, A= Future value = 4042415 PMD = Monthly amount need to deposit r = Monthly Interest rate = 0.833333396 n=No. of months = 28*12 = 336 Therefore, 4042415 = PMD [(1.008333-336-1)(1.008333333)]/0.0083333 PMD = 33687/(0.00833333* 15.2549) PMD = 2190