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14 October, 22:22

Stephanie wants to save for her daughter's education. Tuition costs $12,000 per year in today's dollars. Her daughter was born today and will go to school starting at age 18. She will go to school for 5 years. Stephanie can earn 12% on her investments and tuition inflation is 6%. How much must Stephanie save at the end of each year if she wants to make her last savings payment at the beginning of her daughter's first year of college

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  1. 14 October, 23:19
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    Annual deposit = $3,463.37

    Explanation:

    Giving the following information:

    Tuition costs $12,000 per year in today's dollars.

    Number of years = 18

    She will go to school for 5 years.

    Stephanie can earn 12% on her investments and tuition inflation is 6%.

    First, we need to calculate the cost of each year and the total cost.

    FV = PV * (1+i) ^n

    Year 1 = 12,000*1.06^18 = 34,252.07

    Year 2 = 34,252.07*1.06 = 36,307.12

    Year 3 = 38,485.55

    Year 4 = 40,794.68

    Year 5 = 43,242.36

    Total = 193,081.78

    Now, we can determine the annual deposit required:

    FV = {A*[ (1+i) ^n-1]}/i

    A = annual deposit

    Isolating A:

    A = (FV*i) / {[ (1+i) ^n]-1}

    A = (193,081.78*0.12) / [1.12^18) - 1]

    A = 3,463.37
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