You are currently saving for your child\'s college education. The current cost o

Question

You are currently saving for your child's college education. The current cost of college is $10,000 a year. You expect that college costs will continue to increase at a rate of 5 percent a year. Your child is scheduled to begin attending a four-year college 10 years from now (i.e., college payments will be made at t=10, t=11, t=12, and t=13). You currently have $25,000 in an account which earns 6 percent after taxes. You would like to have all of the necessary savings by the time your child enters college, and you would like to contribute a constant amount at the beginning of each of the next 10 years in order to provide the necessary amount. (You want to make 10 equal contributions starting in Year 0 and ending at Year 9.) How much should you contribute to the account each year in order to fully provide for your child's education?

Explanation / Answer

9suppose you are at t=0,

u must currently start saving say 'x' at the beginning of every year.

yearly collection till the end of 10th year from now y = x[(1.06)^10 + (1.06)^9 + ...+ (1.06)]

now suppose we are the end of 10th year(or beginning of 11th year), i.e. we must now pay 1st fees which has grown upto 10000(1.05)^10.

at t=11 (beginning)

y = 10000[(1.05)^10 + ((1.05)^11)/1.06 +...+ [(1.05)^13/(1.06^3)]

if you equate both sides u get the value of x.

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