Saving for College Case Solution

# Saving for College Case Solution - BADM 7090 Case Solution...

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BADM 7090 Case Solution Saving for College: An Application of Time Value of Money Note: All answers were computed in Excel. Calculations done manually could differ due to round-off error and computational precision. 1. Total annual college costs at the present are \$12,500, and this is expected to grow at a rate of 5%. In 18 years, the cost would be = 18 \$12,500(1.05) \$30,083 This would be the cost for the freshman year, 18 years after birth. For the remaining years, the cost is found by increasing each previous year’s cost by 5%: Sophomore year (19 years after birth) = \$30,083(1.05) \$31,587 Junior year (20 years after birth) = \$31,587(1.05) \$33,166 Senior year (21 years after birth) = \$33,166(1.05) \$34,825 Laid out on a time line, the forecasted college costs are as follows: \$34,825 \$30,083 \$31,587 \$33,166 21 20 19 18 17 2. Under Plan A, they save for 17 years. They need to know how much money they need in their account after the 17 th deposit. Thus, they need to know the value at year 17 of the tuition payments that will come in years 18, 19, 20, and 21. They merely discount these four cost figures back from their respective time points to year 17. +++ =+++= 1234 \$30,083 \$31,587 \$33,166 \$34,825 (1.04) (1.04) (1.04) (1.04) \$28,926 \$29,204 \$29,485 \$29,768 \$117,382 Version: January 3, 2011 Saving for College Case 1

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Thus, they will need to make 17 annual deposits that accumulate to a value of \$117,382 as of year 17. This is a simple ordinary annuity problem using the compound factor for an annuity. + (1 ) 1 n r r Inserting the numbers, ⎛⎞ = ⎜⎟ ⎝⎠ = 17 (1.04) 1 \$117,382 0.04 \$4,953 D D To prove that this is the correct answer, we construct a table similar to the following: Beginning Ending Year Balance Interest Additions Withdrawals Balance 0\$ 1\$ 0 \$ 4 , 9 5 3 \$ 0 \$ 4 2 \$4,953 \$198 \$4,953 \$0 \$10,105 3 \$10,105 \$404 \$4,953 \$0 \$15,462 4 \$15,462 \$618 \$4,953 \$0 \$21,034 5 \$21,034 \$841 \$4,953 \$0 \$26,829 6 \$26,829 \$1,073 \$4,953 \$0 \$32,856 7 \$32,856 \$1,314 \$4,953 \$0 \$39,123 8 \$39,123 \$1,565 \$4,953 \$0 \$45,641 9 \$45,641 \$1,826 \$4,953 \$0 \$52,420 10 \$52,420 \$2,097 \$4,953 \$0 \$59,471 11 \$59,471 \$2,379 \$4,953 \$0 \$66,803 12 \$66,803 \$2,672 \$4,953 \$0 \$74,428 13 \$74,428 \$2,977 \$4,953 \$0 \$82,359 14 \$82,359 \$3,294 \$4,953 \$0 \$90,606 15 \$90,606 \$3,624 \$4,953 \$0 \$99,184 16 \$99,184 \$3,967 \$4,953 \$0 \$108,105 17 \$108,105 \$4,324 \$4,953 \$0 \$117,382 18 \$117,382 \$4,695 \$0 \$30,083 \$91,995 19 \$91,995 \$3,680 \$0 \$31,587 \$64,088 20 \$64,088 \$2,564 \$0 \$33,166 \$33,485 21 \$33,485 \$1,339 \$0 \$34,825 \$0 0 , 9 5 3 The ending balance each year reflects interest paid at 4% on the beginning balance, plus additions and withdrawals. For example, at the end of year 2, the ending balance of \$10,105 carries forward to the beginning balance for year 3. This figure accrues interest at 4% and is increased by the deposit of \$4,953 to equal: + = \$10,105(1.04) \$4,953 \$15,462 Notice how the ending balance in year 21 is zero. Version: January 3, 2011 Saving for College Case 2
3. Under Plan B, the problem is somewhat more complex. They are going to save for 21 years. Thus, they need to know how much money they need to have saved by year 21 at which time they have made their last payment for Kate’s education. This problem will require that they compound the four tuition payments to year 21.

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Saving for College Case Solution - BADM 7090 Case Solution...

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