Which is cheaper: 50% down with 50% loan or 100% loan with 50% immediately paid after signing

Question

I find myself in a position of needing to finance a large purchase. Fortunately, I saved a significant amount in expectation of this expense so I have about 50% of the total cost on hand and allocated. My choice then comes down to one of two options:

1. Pay 50% down and then finance the remaining 50%.
2. Finance 100% and then immediately pay 50% of the value in a lump sum payment.

I am leaning toward option #2 as it seems like this would avoid the expensive part of the loan at the beginning where most of the cost of a single payment goes to interest.

It seems like this should be directly calculable for both cases but I am a little unsure. Case #1 is trivial and just uses the standard formula for interest over the duration of a loan. What I don't understand how to factor in, however, is the 50% lump sum payment for case #2. I cannot simply reduce the principal amount as that is just case #1 and doesn't account for the 'skipped' interest payments.

Some notes:

• Either option doesn't significantly alter the interest rate, which can be kept as constant.
• Loan term would be identical in either case.
• I have planned these costs such that I can continue to over-pay each month with the goal of getting the entire thing paid off in ~2 years.
• None of this involves touching any kind of investment account or retirement.

So, as stated in the title, which is cheaper: 50% down with 50% loan or 100% loan with 50% immediately paid after signing? How can I calculate this?

Answer 1

If there are no prepayment penalties, and they apply all additional payments to principal, then the difference between the two will be the size of your monthly payment, and you'll just pay off the loan faster if you pay the payment for the larger loan. If you paid the same amount each month (meaning you made the larger payment each month on the smaller loan, the two would be completely identical.

The interest portion of each payment is calculated by taking the current principal balance, multiplying by the periodic interest rate (e.g. the annual interest rate / 12 for a monthly payment). Any payment you make above that interest amount goes to reducing the principal, which lowers the interest amount of the next payment, increasing the principal, lowering the next interest amount, etc.

So borrowing the full amount and then immediately paying half down is cheaper because you'll have a higher monthly payment, paying it down faster and paying less interest. If you borrowed half as much and made double the monthly payment each month, they would be exactly the same.

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Say you have a $1,000 loan at 12% interest with a $50 monthly payment (using numbers for simplicity; they may nor may not match a specific amortization table), the interest for the first month will be 1,000 * 1% = $10. The $50 payment will include that $10 of interest and reduce the principal

If you instead take out a $2,000 loan and immediately pay $1,000, the your principal balance is now $1,000, and the math for the interest is the same, but because the initial balance was twice as much, your monthly payment is also twice as much, so you'd be paying $100 per month instead of $50. $10 would still go to interest, and your principal would be reduces by $90 instead of $40, reducing your principal more lowering your interest more, and reducing the number of payments you have to make until you pay the loan off.

There are loans (typically predatory car loans) that apply payments to interest first, meaning the total amount you will pay (principal + interest) is pre-calculated upfront, ant you have to pay off this entire amount regardless of whether you prepay or just make the monthly payment. Avoid these loans like the plague. The only way to get you of these loans it to pay the entire interest amount. With "conventional" loans, all you need to pay off is the principal balance plus any accrued interest to pay off the loan.

Answer 2

In terms of interest paid, both versions are equivalent if you aim for the same payoff time.

Example: $10,000 loan amount, 6% interest rate, 36 month. Monthly payment is $304 and total interest paid is $952.

If you take out a $20,000 loan at 6% loan instead, you would have to take it out over 80 months to get the same monthly payment, which in this case would also be $304. If you pay off $10,000 on day 1 and keep paying $304 you will be done after (just about) 36 months with a total interest payment of $953.

The main difference would probably be in the fees (closing cost, originating cost, make-the-bank-rich fees, etc). If these are based to some extent on the loan amount, taking out the higher loan will be more expensive.

Answer 3

The simple answer is: "They're basically the same." I think the premise of your question is flawed because of a misunderstanding of how term loans work:

I am leaning toward option #2 as it seems like this would avoid the expensive part of the loan at the beginning where most of the cost of a single payment goes to interest.

Although that's true, the amount of interest is based on the remaining principal balance of the loan, and that would be the same in both cases. So the comparison might be something like:

1. $500/month with the first month's breakdown being $100 to principal and $400 to interest.
2. $1000/month with the first month's breakdown being $600 to principal and $400 to interest.

So the total cost in interest is the same. That being said, if you paid the minimum payment each month, you'll pay off of the loan significantly faster with the larger monthly payment, but with the lower minimum, each month you have the option of paying more if you want to, so you could simulate the higher payment on your own without forcing it. For this reason I would personally prefer having the lower minimum payment so if my situation changes in the future I leave my options open.

Side Notes:

1. It might not be possible to immediately make the payment equivalent to the down-payment. It could take some time for the payment to post and you'll probably be charged at least a few days worth of interest. For a large purchase that could be a significant amount of money to basically throw away for little gain.

2. Sometimes forcing the higher monthly payment is attractive, perhaps because you don't think you'll have the discipline to make overpayments yourself when you can. If this is the goal I would still consider the smaller loan amount, but perhaps you can shorten the term. This will bump your payment back up and sometimes shortening the term will lower your interest rate too, which would certainly be worth it compared to paying off a higher interest loan early.

Answer 4

The people saying these would be identical aren't taking into account all the factors. Consider the following two scenarios:

Scenario A:
Step 1: pay 50% down payment
Step 2: take out a loan for the remainder

Scenario B:
Step 1: take out a loan for 100%
Step 2: pay down 50% of the loan

The situation after Step 2 of Scenario A is the same as the situation after Step 2 of Scenario B, except that the state after the respective Step 1 is important. In Scenario B, you are planning on getting to Step 2, but the bank has no assurances of that. You still have the option of staying at Step 1, and no matter how much you're planning on going to Step 2, the bank needs to price the loan based on that. In Scenario A, you've taken the option of not paying the other 50% immediately away from yourself, and that's going to make the loan more attractive for banks. In Scenario B, the bank is going be looking at twice the loan amount, and you're going to have the same income in both scenarios, so you're going to have twice the debt to income ratio. The higher monetary reserves of you having the other 50% will offset this difference partially, but not fully; in Scenario B, you could just spend that money of something frivolous, and there's nothing the bank can do about it, while in Scenario A the bank already has the money in their hands.

I am leaning toward option #2 as it seems like this would avoid the expensive part of the loan at the beginning where most of the cost of a single payment goes to interest.

You're engaging in the fallacy of comparing unlike things. In Scenario B, the initial calculation of the monthly payment will be higher than in Scenario A, because the bank will be basing their calculation on a higher expected principal. Let's use "P_A" to refer to the monthly payment in Scenario A, and "P_B" for the one in Scenario B. If you compare "Put 50% down, and then make P_A each month" to "Put nothing down at first, then prepay 50%, and then pay P_B each month", then the second option will indeed result in less total interest. But if you compare "Put 50% down, and then make a payment P_B each month" to "Put nothing down at first, then prepay 50%, and then pay P_B each month", then the first option will result in less interest. It's the paying more per month, not the prepayment, that is resulting in less interest. Even better would be "Put 50% down, then tell the bank that they can charge you P_B each month". Banks will generally charge lower interest rates if you agree to higher monthly payments.