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A 500 kcal daily deficit is 3500 kcal a week, which at 7700 kcal per kilogram is about 0.45 kg weekly. Losing 13 kg then takes roughly 28.6 weeks, or six and a half months, and a cumulative deficit of 100,100 kcal. The linear projection is optimistic late on, because maintenance requirements fall as weight comes off.
Weekly loss
weekly = daily deficit x 7 / 7700
Weeks needed
weeks = weight to lose / weekly loss
These figures are population-average estimates, not a medical assessment or diagnosis. Body composition equations carry errors of several percentage points, and healthy ranges vary with age, ethnicity, muscularity and medical history. Discuss weight or body composition goals with a qualified clinician or dietitian.
Because energy expenditure declines with body mass and adaptive thermogenesis reduces it further, so a fixed intake produces a shrinking deficit.
Typically 500-750 kcal a day, keeping loss to 0.5-1% of body weight weekly. Larger deficits risk lean mass and micronutrient shortfalls.