Business Math- Annuities

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Ivanthedumbfck

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Elsie Shen wants to withdraw $6,000 at the beginning of every 3 months for 20 years, starting at the date of her retirement. If she retires in 18 years and interest is 4.68% compounded quarterly, how much must she deposit into an account every quarter for the next 18 years, starting now?

Here's what I did, I don't know if i did this right. Oh man this stuff is confusing, i need lots of coffee.

I=0.0468/4=0.0117
n1=20x4=80
n2=18x4=72

FV= 6000[(1.0117)^80-1]/0.0117= 787664.61

PV= PMT[1-(1+i)^-n2]/i
787664.61= PMT[1-(1+0.0117)^-72]/0.0117
PMT= 16,274.29
 
Okay here's my corrected answer:

I=0.0468/4=0.0117
n1=20x4=80
n2=18x4=72

PV= PMT[1-(1+i)^-n1]/i
PV= 6000[1-(1+0.0117)^-80]/0.0117
PV= 310,599.92

FV= PMT[(1+i)^n2-1]/i
310,599.92= PMT[(1+0.0117)^72-1]/0.0117
PMT= $2772.78

 
Ivanthedumbfck said:
Okay here's my corrected answer:

I=0.0468/4=0.0117
n1=20x4=80
n2=18x4=72

PV= PMT[1-(1+i)^-n1]/i
PV= 6000[1-(1+0.0117)^-80]/0.0117
PV= 310,599.92

FV= PMT[(1+i)^n2-1]/i
310,599.92= PMT[(1+0.0117)^72-1]/0.0117
PMT= $2772.78
Click to expand...
The difference between your answer and Denis's answer is when the withdrawal starts. If you notice in the table Denise provides, that there is no interest paid on that last $2805.22 payment. That is the withdrawal of the $6000 starts with the deposit of that last $2805.22 payment. On the other hand, your solution has a quarter's difference between the last $2772.78 and the beginning of the withdrawal of the $6000.

To get Denis's answer, the n2 would be 71 AND then, at the beginning of the next quarter, accumulate your interest (multiply by 1.0117) and add in the extra payment of $2805.22.That is your FV would look like
\(\displaystyle FV = PMT * [1.0117 * \frac{1.0117^{71} - 1}{.0117} + 1]\)
You then immediately start your withdrawals by drawing out the $6000.

The problem seems to say that the way Denise did is is the correct way [the $6000 withdrawal starts "right away" per the problem statement] but it does seem strange that it would work that way [make a deposit to immediately draw it out].

Edit to add: In a hurry this am so forgot that there might be something on the back end also.
 
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