A father is now planning a savings program to put his daughter through college. She is 13, she plans to enroll at the university in 5 years, and she should graduate in 4 years. Currently, the annual cost (for everything - food, clothing, tuition, books, transportation, and so forth) is $13,000, but these costs are expected to increase by 6% annually. The college requires that this amount be paid at the start of the year. She now has $10,000 in a college savings account that pays 8% annually. Her father will make six equal annual deposits into her account; the first deposit today and sixth on the day she starts college. How large must each of the six payments be?
The college fees for the first year of college = 13,000*1.06^5 = $17,396.93
The college fees for the second year of college = 13,000*1.06^6 = $18,440.75
The college fees for the third year of college = 13,000*1.06^7 = $19,547.19
The college fees for the fourth year of college = 13,000*1.06^8 = $20,720.02
Total fees for 4 years = $76,104.89
The 10,000 saved will be = 10,000*1.108^5 = 14,693.28
So remaining amount required = 76,104.89 -14,693.28 = 61,411.61
Let us say amount = X
X*1.08^5 + X*1.08^4 +X*1.08^3 +X*1.08^2 +X*1.08 + X = 61,411.61
7.335929X = 61,411.61
X = 8,371.35
So, each of the six deposits should be worth $8,371.35
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