If you did not live in the house until after the end of the khums year, then the khums is the fifth of the house’s value. If you lived in the house before the end of the khums year, then the house is not a subject to khums. You should pay khums from your savings and the unused gold.
The difference is that paying in installments is a purchase made for a specific agreed-upon price, albeit higher, over a set period; whereas buying on credit is a purchase of something for a fixed price, made through an interest-based loan, and as long as the loan is not fully repaid the interest will apply above the agreed-upon price. Therefore, paying in installments does not involve Riba as defined by the Sharia and is permissible, and paying on credit does involve Riba and is prohibited.