Q1. What is the present value of the cost of college education for 4 children ag

Question

Q1. What is the present value of the cost of college education for 4 children ages 1,3,5, and 7. The current cost of college is $25,000. The children will begin college at age 18 and be in college for 4 years. Education inflation is expected to be 6% and the parents portfolio rate of return is 8%.

A. $294,000

B. $295,000

C. $300,000

D. $305,000

Q2. Using the previous information, how much do the parents need to save annually at year end through the education of the youngest child at pay all college costs.

A. $17,418.31

B. $29,381.57

C. $29,921.11

D. $30,526.52

Can you provide please provide the calculations to solve questions 1 and 2. I want to know the process of how each step resulted in the final answer.

Explanation / Answer

Dear student let us first try to understand what is the concept of present value and education inflation..

the question specifically says what will be the present value of cost of education for four children age 1,3,5 and 7 they all would begin their college at the age of 18 and will remain there for 4 years..

if the cost of college is $25000 at present time
so future value = present value (1+r)n

here future value is the value of education in future
presnet value is the cost of education today which is the current cost
r is the rate of infaltion in eduaction cost
and n is the time frame for which you need the future value

so for child 1 whose age is 1 will be taking education after 17 years in college and would be there for 4 years
so present value for the future after 21 years (18 years minus present age of child add 4yeard which is the college duration so this would be $25000*(1+.06)21

similarily for child 2 whose present age is 3 years

$25000*(1+.06) 19

similarily for child 3 aged 5 years and child 4 aged 7 years
$25000*(1+.06)17    and $25000*(1+.06)15

so present value of future education will be
$25000(1+.06)21+ $25000(1+.06)19+ $25000(1+.06)17 +$25000(1+.06)15 = $305000

so answer for part 1 is option d $305000

now for youngest child how much parents need to save anually
parents rate of return is 8%

and present value of cost of college required is $25000(1+.06)17 = $71250

beacuse 6% is the rate of education cost inflation

and the parent can earn 8% on the amount invested so amount required is $71250 after 17 years
so what amount to be invested now will be $71250 divided by (1+0.08)17
= $17418.31

Answers

solution 1 - option d

solution 2- option a

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