Question

Kathy and Ralph have a 13-year-old daughter who dances ballet. Her dance teacher told her parents that she is a gifted dancer and would probability receive scholarship money when applying to schools of dance. Their daughter wants to attend a prestigious ballet school in London where each entering student receives a $20,000 scholarship towards the school’s $50,000 total 2-year tuition-room-and-board fees. Her parents have decided that if they start saving now, they can accumulate enough funds to pay the remaining fees for her two years at this school. Assuming the fees at the school remain constant from now until she enters and graduates, how much money would her parents need to save quarterly in order to accumulate the necessary amount by her 18th birthday (5 years) if they invest in a CD that earns 3.6% compounded quarterly?

1. In reference to the above, if her parents did not help her out with tuition and she had to borrow that same total amount of money not covered by her scholarship, how much would her monthly loan payments be if her student loan charged 7.2% compounded monthly for a six year loan?
2. Again, in reference to problem #1, her maternal grandparents have decided to help the young dance prodigy by saving $700 semiannually to provide money so she can have funds for flights back home to the US. If they do this for the next 5 years, how much will they have saved if they invest in an account earning 4% compounded semiannually?
3. Again, in reference to problem #1, her paternal grandparents also want to help. They open up a savings account with a $6000 deposit in order to provide our dancer with funds to buy new ballet shoes and new clothes for school. How much money can they accumulate in five years if the savings account earns 1.02% compounded semiannually?

Answer 1

a)
Present value of fees  ( 50,000 - 20,000) x 2	60000
Period = 5 x 4	20
Rate = 3.6%/4	0.90%
PMT = Amount need to be saved per quarter	$3,291.54
b)
Present value of fees  ( 50,000 - 20,000) x 2	60000
Period = 6*12	72
Rate = 7.2%/12	0.60%
PMT = Monthly loan payments	$1,028.71
c)
PMT	700
Period = 5*2	10
Rate = 4%/2	2.00%
Amount saved in 5 years	$7,664.80
d)
Present Value	$  6,000.00
Period = 5*2	10
Rate = 1.02%/2	0.51%
	$6,313.12