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Mizzy Elliott plans to pay her daughter’s tuition for four years starting eighteen (18) years from now. The current annual cost of college is $7,500 and she expects this cost to rise at an annual rate of 5 percent. She assumes that she can earn 6 percent annually in her planning. How much must Missy put aside each year, starting next year, if she plans to make 17 equal payments?

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:

https://brainly.com/question/8008650

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