Question: I need assistance in figuring out how to solve for a problem (step-by-

Question

Question: I need assistance in figuring out how to solve for a problem (step-by-step) so I can understand and explain it to another person. I need to be able to demonstrate what my recommendation is, as well as how I arrived at it. For reference, it's for educational planning.

Assumptions:

-There are two children, age 8 and age 6. Both will need projections.

-$40,000 is available for each child ($80,000 total) that can be invested immedately in year 1

-Assuming the $40,000 is invested for each of the children, I need to figure out how much to tell the parents to invest per year to reach their funding goal.

-Assume the rate of return of investment is 7%

-Assume the rate of inflation on tuition is 4.5%

-Assume that in today's dollars they'll need $35,000 per annum for 4 years (tuition inflation will need to be accounted for).

Tips:

-Create a table similar to that which is depicted, illustrating each of the steps of the calculation for each child.

-Based on all the information contained in the case, calculate the additional annual systematic investment needed for each child

-Pay particular attention to the proper mode of the calculator for each step

Update: There is no format for answer, just please show your work on how you arrived to the answer

Explanation / Answer

We assume that the $40000 available per child is invested at the beginning of Year 1 and hence earns returns for the entire year period. Since we are not also given the age at which the funding is required, we assume it to be 18 years for each child (usual age for college). Now we will first calculate the amount of funds required per child :

Child 1 is aged 8. In 10 years time, they would required $35000 in today dollars each year for 4 years. Adjusted for inflation the tution fee will be : Year 10 = 35000 * (1+4.5%)10 = 54353.93; Year 11 = 35000 * (1+4.5%)11 = 56799.86; Year 12 = 35000 * (1+4.5%)12 = 59355.85 and Year 13 = 35000 * (1+4.5%)13 = 62026.86. The present value of the tution fee for 4 years at the beginning of Year 10 at 7% (rate which they can invest) will be = 54353.93 + 56799.86/(1+7%) + 59355.85/(1+7%)2 + 62026.86/(1+7%)3 = 209914

Now the amount of 40000 invested at 7% will increase to by Year 10 : 40000 * (1+7%)10 = 78686.05

Hence there is a gap of (209914-78686.05) = 131227.95

Let us assume that the family should invest x amount each year which will earn 7% per annum and this should grow to 131227.95 for them to meet their education goal. This is like an annuity and we will use the future value formula to calculate the value of x.

Future value of annuity = Periodic cash flow * [(1+r)t - 1]/r ; where r is the interest rate (7%) and t is time period (10 years). Plugging in the values:

131227.95 = x * [(1+7%)10 - 1]/7%; solving for x we get x = 9497.95 which is the amount they should invest for child 1 to reach the education goal for this child.

Child 2 is aged 6. In 12 years time, they would required $35000 in today dollars each year for 4 years. Adjusted for inflation the tution fee will be : Year 12 = 35000 * (1+4.5%)12 = 59355.85; Year 13 = 35000 * (1+4.5%)13 = 62026.86; Year 14 = 35000 * (1+4.5%)14 = 64818.07 and Year 15 = 35000 * (1+4.5%)15 = 67734.89. The present value of the tution fee for 4 years at the beginning of Year 12 at 7% (rate which they can invest) will be = 59355.85 + 62026.86/(1+7%) + 64818.07/(1+7%)2 + 67734.89/(1+7%)3 = 229231.34

Now the amount of 40000 invested at 7% will increase to by Year 12 : 40000 * (1+7%)12 = 90087.66

Hence there is a gap of (229231.34-90087.66) = 139143.68

In this case also we assume that the family should invest x amount each year which will earn 7% per annum and this should grow to 139143.68 for them to meet their education goal i 12 years. This is like an annuity and we will use the future value formula to calculate the value of x.

139143.68 = x * [(1+7%)12 - 1]/7%; solving for x we get x = 7778.41 which is the amount they should invest for child 2 to reach the education goal for this child.

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