TVM Sum ( 2 sums)

A young couple is planning for the education of their two children. They plan to invest the same amount of money at the end of each of the next 16 years, i.e., the first contribution will be made at the end of the year and the final contribution will be made at the time the oldest child enters college. The money will be invested in securities that are certain to earn a return of 8 percent each year. The oldest child will begin college in 16 years and the second child will begin college in 18 years. The current cost of one year of college is \$10,000 and the parents anticipate college costs will grow at the rate of 8 percent per year through the period when the second child finishes college. These costs must be paid at the beginning of each year. If each child takes four years to complete their college degrees, then how much money must the couple save each year? I am getting PMT as \$9038.15 Today is John’s 30th birthday. Five years ago, Rachel opened a brokerage account when her grandmother gave her \$20,000 for her 25th birthday. John added \$2,000 to this account on her 26th birthday, \$2,500 on her 27th birthday, \$3,000 on her 28th birthday, and \$5,000 on her 29th birthday. John’s goal is to have \$400,000 in the account by her 45th birthday. Starting today, she plans to contribute a fixed amount to the account each year on her birthday. She will make 15 contributions, the first one will occur today, and the final contribution will occur on her 45th birthday. Complicating things somewhat is the fact that Rachel plans to withdraw \$25,000 from the account on her 35th birthday to finance the down payment on a home. How large does each of these 15 contributions have to be for John to reach her goal? Assume that the account has earned, and will continue to earn, an effective return of 10 percent a year. I am getting PMT as \$16,806.25

I am getting 1) 1245.70 per parent to make \$75,555 which should take care of both children thru 6 yrs their combined college. 2) John has to dep \$8,452.44 per year to reach the goal.

Can you show me your calculations… as i am not even near to your ans…

First I’d like to know the real answers or choices at which point it makes sense to explain how arrived at.

I dont have answeres with me… so only have posted to check if i am right or not…

What i have done is here… 1) Period = 16 Interest = 8% PV = 0 Current Cost of 1 year of College = \$10,000 Fees Increment = 8% Time 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 PV 0 274075.42 PMT (9038.15) Fees Requirement at the Beginning of the year: Calculating for Value at end of 16th year : Discount / Int Rate = 8% 16 th Year = 31721.69114 34259.43 17 th Year = 34259.42643 34259.43 18 th Year = 74000.3611 68518.85 19 th Year = 79920.38998 68518.85 20 th Year = 43157.01059 34259.43 21 th Year = 46609.57144 34259.43 Payment at end of each year = 9038.15 2) Interest Rate = 10% Time 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 FV 400000 PV 32,072.87 Deposit 20000 2000 2500 3000 5000 WithDrawal 25000 PMT The value of deposit at time 30 = Present value of withdrawal at t30 = Value Interest Year Amt at t30 Value Interest Years Amt at t30 20000 10% 5 (32,210.20) 25000 10% 5 (15,523.03) 2000 10% 4 (2,928.20) 2500 10% 3 (3,327.50) 3000 10% 2 (3,630.00) 5000 10% 1 (5,500.00) Sum (47,595.90) At time 30 Rachel has 47595.90 in account but will need 15523.03 for futur withdrawal at t35 Thus at time t30 the total = (32,072.87) At time t30, we have PV = 32,072.87 Periods = 15 FV = 400,000.00 Int = 10% PMT = (16,806.25) Payments for next 15 years need to be of \$16806.25

can anyone help me with this TVM sums

The first question: Because the rate of return on the securities where the annuity is invested, and the tuition, increases at the same 8% rate, in fact at the beginning of the year 16 you would need 8 years of tuition (8 years of college tuition, 4 for each child, no matter when paid in the future, when discounted back at the 16th year, 8% is both the return on the securities and the increase in tuition). A year of tuition would be in 16 years: 10,000*1.08^16=34,259.42643~34,258.43, for 8 years this would be 8*34,259.43=274,075.44. You need to make 16 payments at year end, so that in 16 years you would have 274,075.44. This amount includes though the last (16th) payment. Actually, you should look at it as an annuity due (since the end of a year is the beginning of the next year), so put your calculator in begin mode: N=16, I/Y=8, PV=0,FV=274,075.44 compute PMT=8,368.66 The second question: I suppose John is Rachel or this person is called John Rachel. I’m further wondering, if she starts contributing today, when it is her 30th birthday, and the last contribution is made on her 45th birthday, don’t we have 16 contributions? Or do we assume that on her 35th birthday she makes no deposit? Do you have answers? At least we can have some “guessing” start.

1. PMT = 9346.36 2) PMT=16806.25