Let us say someone has $4000 in credit card dept. This person gets an unsecured personal loan with the following terms:

Principal: $5000

Interest rate: 10%

Number payments: 36

Payments: $161.34

Total interest paid on the loan: $808.09

$4000 of the loan is used to pay off credit card debt. The remaining $1000 is being evaluated for an investment opportunity.
For the investment to make since, the return on investment most be greater than the cost of the loan.

In this case the cost of the loan is $808.09. How does one calculate how much of the $808.09 is attributable to the $1000 being evaluated for investing?

The $1000 for investment is 20% of the loan amount, so the amount of interest attributable to the $1,000 investment is 20% of the total interest on the loan. I didn’t double check your number, but if your $808.09 in interests is correct, the amount of interest on the investment portion of the loan is $161.62. You would theoretically want a return on your investment within the loan term that exceeds the sum of the loan principal invested ($1,000) and the interest ($161.62).

Presumably, the rate on this loan is better than the rate on the credit card, so it makes sense to borrow at least $4,000 to pay off the credit card debt regardless of whether you also choose to borrow the extra thousand for the investment. Be careful if you do this though, because many people who borrow to pay off credit cards find themselves running the credit card debt up again. Then they have both the loan and the credit card to repay and they are much deeper in debt.

It’s hard to see why you’d think the answer is anything other than one-fifth.

The interest paid on a $4000 loan is 4/5 of $808. That transaction makes sense if the credit card interest rate is higher, and there is no prospect of finding another way to pay of the credit card fairly soon. Don’t forget the second part, unless the personal loan has flexible terms that allow it to be paid off early without penalty. Although 10% is a much lower interest rate than a credit card, 10% is still a high rate, and you may be losing the flexibility to pay it off more quickly.

The additional $1000 is a separate transaction that should be assessed on its own merits, for which the interest cost is 1/5 of $808.

The only reason that this would not be true would be if there is some economy of scale, i.e. if part of the interest cost is in the form of an “arrangement fee” or something, and the arrangement fee is the same fixed amount for a $5000 loan as for a $4000 loan, implying that the effective interest rate for the first $4000 is higher than the rate for the next $1000.

Bear in mind that this amount of interest is only correct if your investment opportunity is generating cash flow immediately to make monthly payments starting in 1 month. If you won’t pay a 10.5% loan back until the end of the 3 years, the amount of interest to be paid would be more than double this, around 35% of the loan amount.