# Finance or Pay Cash

So, my wife and I are looking at buying a new car about 6 months from now. We've started crunching numbers to see what we can afford and plan to pay cash.

A while back, I heard a strategy when buying a car. Instead of paying cash, try to get a loan with a low interest rate. If you are able to get a low enough rate, it can be profitable to take the loan and invest the cash you have saved up. At the end of the loan period, you will have made more interest on the cash you had saved than you paid on the loan.

Sounds like a good, sophisticated, "I understand opportunity cost", economic approach. Professor James Kearl (of BYU's infamous Econ 110 class) would be proud.

Then I took a closer look at the numbers, and discovered a flaw in the argument.

### Assumptions

Car costs $20,000

The load period is 5 years

The loan interest rate is 5%

The investment interest rate is guaranteed at 6% (after taxes, etc.)

### Naive approach

Total cost of loan (principle + interest): $22,645.48

Total value of investment (principle + interest): $26,977.00

So theoretically we make ~$4,300 by being smart. "Self, Great Day!"

#### Problem

The argument forgot about the monthly payment. It needs to come from somewhere.

### Better Approach

Assuming no other income, we must make the monthly payment from our investment. The payment is $377.42/month.

The total cost of the loan is the same, but the total value of the investment takes a hit, as the principle decreases (and with it the interest amount earned) each month.

If we do the math, after making the final payment, we are left with $512.74 in our account.

Not too bad still. We make 500 bucks. "Self, Not-too-shabby day!"

I decided to explore the case where we have a monthly income. Let's say we have a monthly income surplus of exactly $377.42/month, allowing us to make the monthly payment without affecting our investment. Sounds great!

We pay a total of $22,645.48 and have $26,977.00 in our investment. We make ~$4,300!

### Best approach

What if we paid cash, and decided to invest that $377.42/month instead. So we would empty our investment by paying cash and instead of paying a monthly payment to the bank we would use it to replenish our investment.

So at the end of 5 years:

Total paid for car: $20,000.00

Total in investment: $26,464.27

Total gain: $6,464.27

"Self, Great day!!!!!!!!!"

### Conclusion

Taking the loan and investing the cash appears to not be such a great deal after all. It only seems to make sense if you are (1) expecting no additional income during the loan and (2) guaranteed a high enough interest rate on your investment. Even then it's only a difference of $500. Not sure if that's enough to offset the risk of something going wrong. If you expect to have enough income to make the monthly payments from your surplus, then it is much better to pay in cash upfront and invest the monthly payment amount. It requires diligence, but clearly pays off.Did I miss anything? The assumptions I made may not be very realistic, but I think they are generous enough to show a favorable, yet possible scenario. If things were more generous (like an interest rate of 10% on the investment) then perhaps the numbers would change.

Thoughts?

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