Question 1140784: Help please! I'm confused on how to get the yearly contribution. Kelly and Sam plan to send their daughter to college. To pay for this they will contribute 10 equal yearly payments to an account bearing interest at the APR of 4.2%, compounded annually. Four years after their last contribution, they will have begin the first of five, yearly withdrawals of $49,300 to pay the college expenses. How large must their yearly contributions be?
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Kelly and Sam plan to send their daughter to college.
To pay for this they will contribute 10 equal yearly payments to an account bearing interest at the APR of 4.2%, compounded annually.
Four years after their last contribution, they will have begin the first of five, yearly withdrawals of $49,300 to pay the college expenses.
How large must their yearly contributions be?
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there are 3 stages to this problem, the 10 yr accumulation phase, the 4 yr earning phase, the 5yr payout phase.
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To the nearest $
Start with the last phase, how much will you need initially to pay 49.3k a yr for 5 years earning 4.2%?
Using the finance feature on my Ti83 I got: $218,247
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The earning phase, how much will need initially, to get $218,247, earning 4.2% in 4 yrs.
Again using the finance feature I got: $185,130
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The accumulation phase, what will have have to deposit annually to accumulate $185,130
Using the same method: $15,277 a year for 10 yrs earning 4.2% must be deposited
:
Each one of these calculations has a rather complex formula to calculate it, is that what you want?
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website! Help please! I'm confused on how to get the yearly contribution. Kelly and Sam plan to send their daughter to college. To pay for this they will contribute 10 equal yearly payments to an account bearing interest at the APR of 4.2%, compounded annually. Four years after their last contribution, they will have begin the first of five, yearly withdrawals of $49,300 to pay the college expenses. How large must their yearly contributions be?
I do agree with the other person as far as the calculations that are needed to arrive at each annual contribution. However, I disagree with him using the PRESENT VALUE (PV) of AN
ORDINARY ANNUITY, since payment for college is usually made before college begins, not after. Therefore, in my opinion, the PRESENT VALUE of AN ANNUITY DUE should be used instead.
So, during the 5-YEAR distribution-period, instead of using the PRESENT VALUE of AN ORDINARY ANNUITY of $218,247.16, the PRESENT VALUE of AN ANNUITY DUE of $227,413.55 should be used.
To accumulate $227,413.55 in the 4 years after the 10 annual contributions cease, we’d need the PV of a FV amount of $227,413.55, at a rate of 4.2%. This is: $192,905.88
Now, to accumulate $192,905.88 in 10 years of equal annual contributions, we’d need each ANNUAL PAYMENT, based on a FV ORDINARY ANNUITY amount of $192,905.55, and at an annual interest rate of 4.2%.
This annual payment/contribution is: 
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