A father wants to set aside money for his 8-year old daughter\'s future educatio

Question

A father wants to set aside money for his 8-year old daughter's future education, by making monthly deposits to a bank account that pay's 8 % per year, compunded annually. What equal monthly deposits must the father make- the first 1 month after her 9th birthday and the last on her 17th birthday-in order for her to withdraw $4000 on each of her next four birthdays (the 18th through the 21st)?

I was provided with the answer. $103.80
But, I would like to know the steps through the problem that get me to that solution?

Explanation / Answer

step 1 A = P[i/(1-(1+i)^-n)] 4000 = P[.08/(1-1.08^-4)] P = $13248.50 step 2 F = A[((1+i)^n-1)/i] **note: that the future for step 2 is equal to the principal found in step 1** $13248.5 = A[(1.08^10-1)/.08] **note: n now becomes 10** A = $1245.56 however due to the fact that the dad is depositing every month we need to divide A by 12. Therefore the amount he has to pay each month is $103.80

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