Well… it depends. Generally speaking, money in hand today is worth more than money in the future. $92k earning 3% would equate to $107k in 5.5 years. You will certainly be better off if you can earn more than 3%. However, will you actually be able to achieve this within your risk tolerance and time frame. Investing in anything implies a certain amount of risk that you will not achieve a target return.
Consider the impact of taxes and inflation. Even if you can earn a 3% return, income taxes, capital gains taxes, and inflation will eat away at it. Do you need the money now or can you wait 5.5 years or longer before using it?
Apologies as your question seems simple enough but it really brings up a lot of other questions. Consult with a fee-only advisor to evaluate your tax and risk profile to see if this makes sense for you.
One final question for you… having been through this personally and with clients, a set amount of child support payments only addresses basic needs. If your ex pays you a set lump-sum, what are the implications when other unanticipated needs and expenses arise? This is an emotional and personality issue that can be difficult to quantify. An advisor can help you navigate this mine field.
As John points out, there are a lot of moving parts to this question. The approach I'd recommend is to first decide how much investment risk you're comfortable taking, if you were to invest the lump sum of $92k. If you're comfortable taking a fair amount of risk in your portfolio, the 8.5% your ex-husband mentioned is not unreasonable. Professionals estimate average stock market returns to be between 7% and 9% in the long run.
To your point, it could be better to accept the lump sum and put this money to work, but only if you're comfortable bearing the added investment risk. If you're more conservative, and uncomfortable with the possibility that a portfolio invested in stocks could fall by 25% or more at any given time, the steady flow of payments for the next 5.5 years might be the better option.
There are other factors at play, but this is the framework I'd start with.
You should weigh your options carefully. Typically a lump sum of money in hand now is worth more than installment payments over time. The biggest reason for this is the ability of that lump sum to grow at compounded rates. In your question you mentioned that these are child support payments. Before you decide to accept a lump sum you should consult with an attorney to determine if frequent reviews of financial circumstances are required by the laws in your state. If they are required, say annually, you might be entitled to less child support later down the road. You should ensure that if you take the lump sum that your ex-husband signs a document that provides for no recourse so that he can not come back after any of those funds later.
In regards to the other part of your question, you should consider what your current interest rate is on your mortgage. If it is high and is causing your monthly mortgage payment to be a cash flow strain then I would consider using some of the lump sum to refinance your mortgage at a lower rate. This will potentially reduce the total amount you pay for the mortgage over time and the monthly cash flow requirement to service the loan.
If your mortgage rate is already low then you should look at how much investment risk you are willing to take. Given that level of risk and the anticipated return, will you earn more than the rate of your interest on your mortgage and make sure to factor in taxes. The final consideration I think you should have is will you require any of the lump sum to support you and your child(ren)'s monthly living expenses? If so, you should look at structuring any investment in an income generating portfolio, not a growth portfolio as you may be forced to sell investments when they are down to support yourself.
Good Luck, Mark