Question

Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7%. The parents deposit $2000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to:A) $42,825B) $97,331C) $67,998D) $103,063

Answer 1

Answer:

$97,331.30

Explanation:

To calculate the amount available on the daughter's 18th birthday the following should be taken into cognisance

First, the yearly deposit increases by 5% every year, therefore year one is $2,000 but year 2 is $2,000 x1.05= $2,100 and continuing like that.

Secondly, the total deposit pre year is calculated as annual deposit for the year (1+interest rate)∧year on a descending basis.

It is therefore as follows;

Years Annual deposit    Total value of deposit including interest

1           $2,000.00            $2,000(1+0.07)∧17= $6,317.63

2           $2,100.00            $2,100(1+0.07)∧16= $6,199.54

3           $2,205.00            $2,205(1+0.07)∧15=$6,083.66

4           $2,315.25            $2,315.25(1+0.07)∧14=$5,969.95

5           $2,431.01            $2,431.01(1+0.07)∧13=$5,858.36

6           $2,552.56            $2,552.56(1+0.07)∧12=$5,748.86

7           $2,680.19            $2,680.19(1+0.07)∧11=$5,641.41

8           $2,814.20            $2,814.20(1+0.07)∧10=$5,535.96

9           $2,954.91            $2,954.91(1+0.07)∧9=$5,432.48

10           $3,102.66            $3,102.66(1+0.07)∧8=$5,330.94

11           $3,257.79            $3,257.79(1+0.07)∧7=$5,231.30

12           $3,420.68            $3,420.68(1+0.07)∧6=$5,133.52

13            $3,591.71            $3,591.71(1+0.07)∧5=$5,037.56

14            $3,771.30            $3,771.30(1+0.07)∧4=$4,943.40

15            $3,959.86            $3,959.86(1+0.07)∧3=$4,851.00

16            $4,157.86            $4,157.86(1+0.07)∧2=$4,760.33

17            $4,365.75            $4,365.75(1+0.07)∧1=$4,671.35

18            $4,584.04            $4,584.04(1+0.07)∧0=$4,584.04

Total     $56,264.77                                                $97,331.30