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Sagot :
The amount Missy Elliot should put aside each year to make payments
for tuition in 18 years time at is $2,757.45.
How can the required amount to be set aside each year be calculated?
Year at which the child will start college = 18 years from now
Current annual cost of college = $7,500
The annual increase in tuition = 5%
Number of years of college = 4 years
Therefore;
[tex]A_{18} = \mathbf{7,500 \times \left(1+\dfrac{0.05}{1} \right)^{1 \times (18 )}} \approx 18,049.64[/tex]
[tex]A_{19} = 7,500 \times \left(1+\dfrac{0.05}{1} \right)^{1 \times (18 +1)} \approx \mathbf{18,952.13}[/tex]
[tex]A_{20} = 7,500 \times\left(1+\dfrac{0.05}{1} \right)^{1 \times (18 +2)} \approx \mathbf{19,899.73}[/tex]
[tex]A_{21} = 7,500 \times \left(\left(1+\dfrac{0.05}{1} \right)^{1 \times (18 + 3)} \approx \mathbf{20,894.72}[/tex]
The total cost ≈ 18,049.64 + 18,952.13 + 19,899.73 + 20,894.72 = 77796.22
The percentage earned annually = 6%
Therefore;
The present value is therefore;
[tex]PV = \mathbf{\dfrac{77796.22 }{\left(1+0.06 \right)^{17} }} = 28,890.75[/tex]
The annual payments are therefore;
[tex]Annual \ payment = \dfrac{28,890.75 \cdot \left(0.06\right) \cdot \left(1+0.06 \right)^{17} }{\left(1+0.06 \right)^{17} - 1} \approx \mathbf{2,757.45}[/tex]
The amount Mizzy Elliot should put aside each year is therefore approximately $2,757.45
Learn more about annuity here:
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