Tuition-pay monthly or lump sum with discount, help me calculate the difference!!

[berlinsmommy]

I don't know why I just cannot get this, but maybe you guys and gals can help me.

Berlin's school has two options for tuition payment: I can either pay $4,100 on June 1st or I can pay $381.85/month for 11 months starting on June 20 and going through April 20 (actually last payment is $381.50, but if we get so close that the 35c is a factor I'll pay monthly. I know that the simple math is that I get a $100 break for paying in full, but what about the "opportunity cost" of that money? To pay in full I will drain our Money Market Account, which currently pays 5.11% but the rate fluctuates. To make calculations simple, If I were to keep the $4,100 in the account at 5.11% and drew out $381.50/month for 11 months, how much interest would I earn in that 11 months?

Any other considerations I may be missing?

[jr08]

Using Excel -- you end up about even, with a couple dollars more keeping it in the account. You might need to add in postage and hassle factor.

Pmt Balance Interest
Payment Balance Interest
1 $3,735.61 $17.46
2 $3,369.67 $15.91
3 $3,002.17 $14.35
4 $2,633.10 $12.78
5 $2,262.46 $11.21
6 $1,890.25 $9.63
7 $1,516.45 $8.05
8 $1,141.05 $6.46
9 $764.06 $4.86
10 $385.47 $3.25
11 $5.26 $1.64

Total Interest About $105.50 with leaving it in the account. So the difference is about $5.50 between paying it off early (with the $100 off) or keeping it in the account earning interest. If you had to pay postage this goes down to less then $1. Hope this helps.

[TheWoman]

I am going to figure this compounded daily as that is how many banks work. If not compounded daily than the figures are slightly different, but probably not that much.
Assuming that the interest rate stays the same you would have these amounts in your account on the following days
June 1 = $4100
June 19 = $4110.92
June 20 = $3729.07 (first payment made)
July 19 = $3744.76
July 20 = $3362.91 (second payment made)
Aug 19 = $3377.54
Aug 20 = $2995.69 (third payment made)
Sept 19 = $3008.72
Sept 20 = $2626.87 (fourth payment made)
Oct 19 = $2637.92
Oct 20 = $2256.07 (fifth payment made)
Nov 19 = $2265.89
Nov 20 = $1884.04 (sixth payment made)
Dec 19 = $1891.96
Dec 20 = $1510.11 (seventh payment made)
Jan 19 = $1516.68
Jan 20 = $1134.83 (eighth payment made)
Feb 19 = $1139.77
Feb 20 = $757.92 (ninth payment made)
March 19 = $760.89
March 20 = $379.04 (tenth payment made)
April 19 = $380.69
April 20 = -$.81 (last payment made)

So--it is almost identical, within a dollar, so it should really come down to other considerations. (I didn't include the stamps required to mail in those extra 10 payments--that comes to $3.90, so it is really $4.71 cheaper to pay in advance)

1) It is far easier to just pay once instead of every month
2) If you pay month to month and have an emergency you could tap the money market account and then pay it back over time. If you pay all at once you don't have that option.
3) What happens if you pay in full and then decide not to keep your child in that school for the whole year? Would you get the unused part of your money back? Sometimes you can't predict the twists and turns of life and need to change plans.
4) If the interest rate increases you will do better with the month to month, if it decreases the one time payment will be attractive. Either way it is probably not going to be a huge difference unless rates go WAY up.

[TheWoman]

While I was figuring jr08 posted--the different numbers are because jr08 did the problem the way you asked to simplify it, and I did it the way it works in your origional story. Either way the results are similar.

I have always been a bit compulsive to figure things EXACTLY. (I did the whole thing to 11 decimal places. The real answer is -$.80732332832, though the bank would probably round along the way and that would change it a bit) It is driving me crazy that I don't know for sure exactly what the interest rate will be!

[kurlisola]

With the difference so small, I'd make payments. Why? You never know what is going to come up & I prefer to keep my money in my pocket for as long as possible.

[berlinsmommy]

Ok, thanks everyone for the help, I think I'm going to stick with monthly since like kurlisola said, I have that money available. Also, the payments on the 20th are automatic withdrawl, so I don't have stamps or hassle, and not that it makes a huge difference (so TheWoman doesn't need to redo all the calculations) but if the 20th is a weekend or a holiday it comes out later, not earler.

As far as the if we move or she doesn't go to school there thing, it is an annual contract, so we'd have to pay it in full even if she stopped going there, the monthly payment isn't really representative of paying for her months there.

[too-old-now]

Is there a charge for automatic withdrawal from your account? Some places charge for stuff like that. Do they give you mailing envelopes if you want to mail it yourself - things like these can also offset/contribute postage, etc. Another thing to consider is any fee if you change your bank, and automatic withdrawal comes from a new account?

If you mail it yourself and make a payment 5 days late, do they charge you more interest? How about 10 days late? The orthodontist used to give an automatic 10 day grace period, until they found too many folks were dropping of their monthly payment in person on the last day of the grace period - they were avoiding the interest charge, yet they still had use of their money. Instead of increasing his overall charge - which the insurance companies would not let him do - he lowered the grace period from 10 days to 5 days.

DW pays all of our bills, and she knows when they must be mailed to get their before the grace period ends. The bill may come in on the 21st, not be due until the 1st of the following month, but if the grace period is until the 10th then we won't mail it until the 5th or 6th. There are usually 4 or 5 pending bills at any given time, she writes the targeted mail date on the back of the envelopes.

[kurlisola]

Why all the talk about mailing the payment or automatic deductions? Heck, I just send the check with my daughter. She's there every day afterall-lol!

[MaryMary]

Why all the talk about mailing the payment or automatic deductions? Heck, I just send the check with my daughter. She's there every day afterall-lol!

I'm glad someone is taking care of timely paying my fixed expences for free, that make HUGE difference for me. My DD may keep carrying the envelope with a check for a few days, forget to give it to the office, I may forget to write that check in time, etc. etc. etc. If it is free of extra charge, I'm for scheduled payments.
There are services out there who take care of collecting tuition for schools. They charge parents arm and leg, even more if payments will be drawn from charge card, but if school decides they want to go with them we have no choice..

[berlinsmommy]

There are services out there who take care of collecting tuition for schools. They charge parents arm and leg, even more if payments will be drawn from charge card, but if school decides they want to go with them we have no choice..

I'm pretty happy with this service. I did pay either a $25 or $35 "setup" or some sort of fee, but it truly was one time, as in once forever, so we paid it about 2 yrs ago when we set up the daycare (which is at school, she goes to school and daycare at the same place since its a private school). Plus with daycare you pretty much have to do the automatic payments, there is no "lump sum" option because unlike the all or none tuition, you actually pay for what you use with daycare, so our amount had 4 adjustments last year and will have at least 2 adjustments per year, so I don't incur any fees regardless of which way I structure the tuition payment.

As for sending her with a check, that is not an option. Our two choices are the auto withdrawls on the 5th or 20th (I choose 20th, hey, 15 extra days of interest for me per month) or lump sum on June 1.