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Kerry and Rob just had their first child, Helene. Being financially responsible

ID: 2775477 • Letter: K

Question

Kerry and Rob just had their first child, Helene. Being financially responsible parents, they want to start saving for Helene's college education so that they will have $355,000 by the time she is 18. Assuming that they have $10,000 in a bank account that pays 5% interest compounded monthly today, how much must they add to the account each month to have $355,000 by the time Helene is 18?

approx. $854

approx. $1021

approx. $743

approx. $655

approx. $946

approx. $854

approx. $1021

approx. $743

approx. $655

approx. $946

Explanation / Answer

Answer:

Amount in bank account when helene is 18

= (FV of amount all ready in bank account at t=18) + (FV of annuity deposit every month till t=18)

Now FV of single deposit = PV(1+r)n and FV of an annuity = Annuity[{(1+r)n-1}/r], where r =interest rate per period, n= no of periods

=> $355,000 = $10,000(1+ 0.05/12)18*12 + "X" [{(1+ 0.05/12)18*12 -1} / (0.05/12)]

=> $355,000 = $24,550 +  "X" [{(1+ 0.05/12)216 -1} / (0.05/12)]

=> $330,450 = "X" [{(1+ 0.05/12)216 -1} / (0.05/12)]

=> X = $330,450/349.2 = $946. 3 (option- D)