# What would the formula for loan payoff with daily compounded interest and paid 5 days per wk?

I'm interested in calculating the impact of making payments on my student loans daily (5 payments per wk).

For example my current loan is 50,000\$ @ 5.05% interest compounded daily. The term of the loan is 7 years. I would like to pay as frequently as possible to minimize the daily interest compounded. I would also like to see what the potential savings over the course would be over making normal monthly payments.

Thanks!

• what does 5.05% interest mean? how exactly it is applied? As discussed somewhere here it can change things – aaaaaa Feb 11 at 0:12
• Paying daily only makes sense if you receive this money daily, which is rarely the case. The paycheck is usually once a month, twice a month, every other week, etc. Then, pay right after you've received the money. That minimizes the interest. – void_ptr Feb 11 at 0:20

With any loan, you save the most money when you pay as much as you can as early as possible. It doesn't matter if the loan is compounded monthly, daily, or any other period.

For example, let's assume that the loan you are talking about is compounded daily, and that these interest charges are added to your loan balance daily. (This is unusual.) Let's also assume the following:

• You get paid weekly.
• You just got paid.
• Out of every paycheck, you are planning on sending \$100 to go toward paying off your loan.

Your choices are to either send in \$100 immediately, or to spread it out into 5 equal payments of \$20 each, one each day. Which will result in smaller interest charges?

Of course, it would be sending in the \$100 immediately, as no portion of that \$100 will be subject to interest charges for the next week.

Now, if you get paid weekly, but decide to save up that \$100 each week and only send in \$400 every four weeks, then you have lost a little interest because that \$100 you could have sent in a few weeks earlier has been accumulating interest charges over that time.

When the payment frequency is uneven, you are probably going to need to build a spreadsheet to calculate the total interest paid, paid, but if you want to see the effect, you could choose a daily payment frequency. I don't think the difference is as dramatic as you think it will be.

With a standard monthly compounded loan, the payment would be about \$707.87 per month, for a total paid of about \$59,461, or \$9,461 of interest.

With a daily compounded loan, the daily payment would be \$23.22, for a total paid of \$59,360, or \$9,360 paid in interest. If you paid 5 days a week instead of 7, the total will be somewhere in between the two (closer to the \$9,360).

So paying daily, you save about \$100 over 7 years. Is having to make daily payments really worth that hassle?

To expand on the other answers here, the main point is that you should pay as much money as you can as early as you can because that reduces the principal value of the loan from which daily compounded interest is calculated.

With a 5.05% loan compounded daily, you take that 5.05% and divide it by 365 (the number of days in a year) 0.0138% and multiply that by the principal balance \$50,000 which gives you a daily interest charge of \$6.92.

If you pay that loan down by \$1,000 on the first day of the month, you now calculate the daily interest of 0.0138% x \$49,000 which is \$6.78.

Is it better to have \$6.78 compounded daily that month, or is it better to pay \$6.92 in interest on the first day, \$6.91 on the second day, \$6.90 on the third day, etc.?

It is far better to pay more as early as possible because that reduces the amount of interest compounded. That's also why, by paying 1 extra payment each year on a 30 year mortgage, you can pay it off 4 years sooner and save 17.5% on the total interest paid.