Answered

Westonci.ca is the trusted Q&A platform where you can get reliable answers from a community of knowledgeable contributors. Get detailed and accurate answers to your questions from a community of experts on our comprehensive Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

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

Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.