You will make more money by offering installments (in addition to a full pay option).
Psychology: Some people prefer to spend the payments out. Or maybe they just have cash flow reasons.
Either way, almost always, a payment plan will net profit more money.
The cash will flow slower (depending on the financing partner), but the overall number of sales will go up because you’ll increase the conversion rate. (CVR)
And if you have a strong back-end, you will increase the number of clients that come to you, who you can then up-sell.
Final tip: Like the golden rule of getting your message delivered.
A golden rule is to make sure you can collect cash.
^ It seems self-evident, but I've seen a number of instances when people mess this up.
Example 1: People will wreck their deliverability for short-term sales (They then fail to deliver their message and shoot themselves in the foot).
Example 2: people take their financing partner for granted. Maybe their sales guys break policy, or they over-sell on the front, and refunds increase. If the financing partner finds out (or you trigger a review), then you'll have a fun time trying to run a business when you can't collect cash.