Question

Lauren is the proud mother of a new baby girl and plans to send her daughter to college 19 years from now. Lauren wants to make a deposit each summer in a special account at her bank which pays 10% (compounded annually) so that she will have enough money set aside that she can withdraw $20,000 at the beginning of each year to pay tuition, room and board, etc., for each year of her four-year education. How much will Lauren have to deposit at the end of each year in order to have enough to pay for her daughter's education? (Note: There will be 19 total deposits and the first deposit will be made in one year. Also, the last deposit will be made the day before the first withdrawal.)

                                                                                                         20,000 20,000 20,000 20,000

           

|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|__|

0        1         2         3          4         5         6         7          8         9        10       11       12        13      14      15       16      17        18       19      20       21     22        23      24        25

     pmt?……………………………………………pmt …………..pmt…………………………..pmt?

Hint: 0-19: ordinary annuity, you deposit PMT every year for 19 times;

19-23: annuity due, you withdraw 20,000 every year for 4 times.

Can you get the PVA of those four 20,000 @ point 19? The number you get is the future value of those 19 pmts. Then use that value as FV of the ordinary annuity (the 19 pmts), can you get the PMT?

a. 1,363.14

b. 1,379.89

c. 1,306.64

d. 1,312.84

e. 1,321.12

*Also in our class we required to use the 10bll calculator, so if it can be explained how to be solved that way perfect if not its ok

Answer 1

Money required at end of 19 year for college fund is annuity amount of $ 25,000 for 4 years.

So,

Year	Cash Flow	PVIF@10%	PV of cash flows
0	20000	1	20000.0
1	20000	0.909	18181.8
2	20000	0.826	16528.9
3	20000	0.751	15026.3
		PV =	69737.0

Total cash flows required at year 19 , $69,737.

Now, this is FV that we require after 19 years.

So, at year 0

I = 10, N = 19, FV = 69,737, PV =0

PMT = ?

PMT = $1,363.14

Lauren has to deposit $ 1,363.14 at the end of each year in order to have enough to pay for her daughter's education.

Answer is Option A.