Your client has two children. The younger one just turned 2, and the older one j
ID: 2718952 • Letter: Y
Question
Your client has two children. The younger one just turned 2, and the older one just turned 4. They are expected to go to college when they turn 17. The college expenses are expected to be $25,000 per year for the older child and $30,000 per year for the younger child, for four years, and payable at the beginning of each year. Your client is planning to start a college savings account with an initial deposit of $5,500 today. Then, she can make monthly deposits of $500 with the first deposit in exactly one month, and each consecutive deposit to take place at the end of each month until the first child starts college. The proceeds in the account will be invested in a mix of risky securities with an average expected return of 9% until the first child starts college. Thereafter, the funds will be shifted to a safer account that is expected to generate a mere 6% annually. Your client is planning on taking a well deserved vacation as soon as the first child is off to college. Are there going to be any funds available in the account for that purpose that can be withdrawn (when the oldest child is off to college) without jeopardizing the payouts for the college expenses of the two children? If yes, how much? If no, how much will she be short of her goal?
Explanation / Answer
Age of the older child = 4 years
Age of the younger child = 2 years
Age at which children are expected to attend college = 17 years
Time till first child attends college = 17 – 4 = 13 years
Time till second child attends college = 17-2 = 15 years
Period of College study = 4 years
For First Child
Annual expected college fee P = $ 25,000 per annum payable at the beginning of the year
As the funds will be shifted to a safer account once the first child starts attending the college, the required rate of return to be used should be rate of return on safer account which is 6%
Therefore required rate of return r = 6% or 0.06
Period of college education = 4 years
Total value of college fee required for four years for the first child at the start of college education can be calculated using the below formula
Present Value of amount = P + P * [(1-(1/(1+r)^(n-1)))/r]
Substituting the values from above
Present value of the amount PV1 = 25000 + 25000 * [(1-(1/(1+0.06)^(4-1)))/0.06]
= 25000 + 25000 * [(1-(1/(1.06)^3))/0.06]
= 25000 + 25000 * [(1-(1/1.191016)/0.06]
= 25000 + 25000 * [(1-0.839619)/0.06]
= 25000 + 25000 * (0.16038/0.06)
= 25000 + 25000 * 2.673
= $ 91825.29874 or $ 91,825.30 (rounded off)
For Second Child
Annual expected college fee P = $ 30,000 per annum payable at the beginning of the year
As the funds will be shifted to a safer account once the first child starts attending the college, the required rate of return to be used should be rate of return on safer account which is 6%
Therefore required rate of return r = 6% or 0.06
Period of college education = 4 years
Total value of college fee required for four years for the first child at the start of college education can be calculated using the below formula
Present Value of amount = P + P * [(1-(1/(1+r)^(n-1)))/r]
Substituting the values from above
Present value of the amount = 30000 + 30000 * [(1-(1/(1+0.06)^(4-1)))/0.06]
= 30000 + 30000 * [(1-(1/(1.06)^3))/0.06]
= 30000 + 30000 * [(1-(1/1.191016)/0.06]
= 30000 + 30000 * [(1-0.839619)/0.06]
= 30000 + 30000 * (0.16038/0.06)
= 30000 + 30000 * 2.673
= $ 110,190.3585
Since the second child starts college education 2 years after the first child we need to find the present value of $ 110,190.3585 to arrive at the total value of funds required for college education of two children
Present value of the second child college fee requirement at the beginning of first child college education PV2 = $ 110,190.3585 / (1.06)^2 = $110,190.3585/1.1236 = $ 98,069.0268
PV2 = $ 98,069.03 (rounded off)
Hence the total amount required to be available for college education of both children at the start of the college education of first child is
Total amount required for college education = PV1 + PV2 = $ 91,825.30 + $ 98,069.03
Total amount required for college education = $ 189,894.33 ----- (1)
The amount given above is the required amount for college education 13 years from now when the first child goes to college.
Initial Deposit = $ 5500
Period of Initial Deposit = 13 years
Expected rate of return = 9% or 0.09
Value of initial deposit after 13 years = $ 5500 * (1+0.09)^13 = $ 5500 * 3.0658 = $ 16,861.93
Monthly Deposit A = $ 500
Period of deposit starts 1 month after the initial deposit and continues monthly till the first child goes to college
That is the monthly deposit will continue for 13*12 – 1 = 155 months
Expected rate of return r = 9% or 0.09
Value of monthly deposits after n =155 months can be calculated using the below formula
Future value of annuity = periodic payment * [((1+r)^n – 1)/r]
Substituting the values from above
Value of monthly deposits = $ 500 * [((1+0.09/12)^155 – 1)/(0.09/12)]
= $ 500 * [((1+0.0075)^155 – 1)/(0.0075]
= $ 500 * [((1.0075)^155 – 1)/(0.0075]
= $ 500 * [(3.18408651886-1)/0.0075]
= $ 500 * (2.18408651886/0.0075)
= $ 500 * 291.210203
= $ 145,605.1013 or $ 145,605.10 (rounded off)
Total Value of Savings = Value of Initial Deposit + Value of monthly deposits
= $ 145,605.10 + $ 16861.93
= $ 162,467.03 --- (2)
Expected short fall =(1) – (2) = $ 189,894.33 - $ 162,467.03 = $ 27,427.30
The expected savings from the plan are not sufficient to meet the expected college expenses for the children. The shortfall for education is $ 27427.30. The expected cost of vacation would be over and above the shortfall for education given above.
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