From beginner to expert, IDNLearn.com has answers for everyone. Discover reliable and timely information on any topic from our network of experienced professionals.
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
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.
