# How much more will your parents have to invest each year for the next five years to have the funds for her education? How much money will your parents have at the end of three years to help you with graduate school, which you will start then?

1 Your younger sister, Jennifer, will start college in five years. She has just informed your parents that she wants to go to Penn State U,. which will cost $18,000 per year for four years (cost assumed to come at teh end of each year). Anticipating Jennifer's ambitions, your parents started investing #3,000 per year five years ago and will continue to do so for five more years.

How much more will your parents have to invest each year for the next five years to have the funds for her education? Use 10 percent as the appropriate interest rate throughout the problem (for discounting or compounding).

2. Jennifer (from problem 1) is now 18 years old (five years have passed), and she wants to get married instead of going to college. Your parents have accumulated the necessary funds for her education.

Instead of her schooling, your parents are paying $7,000 for her current wedding and plan to take year-end vacations costing $2,000 per year for the next three years.

How much money will your parents have at the end of three years to help you with graduate school, which you will start then? You plan to work on a master's perhaps a Ph.D. If graduate school costs $18,930 per year, approximately how long will you be able to stay in school based on these funds? Use 10 percent as the appropriate interest rate throughout this problem. (Round all values to whole numbers.)

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Annuity= $3,000

Therefore, future value= $18,315 =3,000. x 6.1051

Next we find the future value of this sum at the end of 5 years

n= 5

r= 10.00%

FVIF (5 periods, 10.% rate ) = 1.61051

Present value= $18,315

Therefore, future value= $29,496 =18,315.x1.61051

Thus the shortfall at the end of 5 years= $27,562 =57,058.-29,496.

Then we find the annuity whose future value= $27,562

n= 5

r= 10.00%

FVIFA (5 periods, 10.% rate ) = 6.1051

Future value= $27,562

Therefore, annuity= $4,515 =27,562. / 6.1051

Answer: parents will have to invest each year for the next five years an amount equal to $4,515

This is an additional $1,515 =4,515.-3,000.

over the $3,000 that they have invested over the past 5 years

We can check the answers

r= 10%

Year Amount at the beginning of year Principal + interest at the end of year Withdrawal at the end of year Deposit at the end of year Amount at the end of ...