Your younger sister, Brittany, will start college in five years. She has just in
ID: 2683971 • Letter: Y
Question
Your younger sister, Brittany, will start college in five years. She has just informed your parents that she wants to go to Eastern State U., which will cost $30,000 per year for four years (costs assumed to come at the end of each year). Anticipating Brittany's ambitions, your parents started investing $5,000 per year five years ago and will continue to do so for five more years. Use 10 percent as the appropriate interest rate throughout this problem (for discounting or compounding).How much more will your parents have to invest each year for the next five years to have the necessary funds for Brittany's education?
Explanation / Answer
present Value of annuity
PVA=A[1-(1+i)-n/i] =30,000*[1-(1+0.1)-1/0.1]
PVA=30,000*3.17 =$95,100
Accumulation based on investing $5,000 per year for 10 years.
future value of annuity
FVA=A[(1+i)n-1/i] =5,000[(1+0.1)10-1/0.1]
FVA =5000*15.937 =$79,685
Additional funds required 5 years from now when Brittany starts college.
Additional funds required in 5 years =PVA-FVA =95,100-79,685 =$15,415
Additional annual contribution required between now and the time Brittany starts college in 5 years.
FVA =A[(1+i)n-1/i]
15,415 =A[(1+0.1)5-1/0.1]
A=15,415/6.105=$2,525
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