A rise in the interest rate will generally result in people consuming more when they are old if the substitution effect outweighs the income effect.

When the interest rate rises, the substitution effect makes saving more attractive because the return on savings is higher, leading individuals to work and save more during their working years and consume more in retirement. If this substitution effect outweighs the income effect (which might make individuals feel wealthier and thus consume more immediately), people will indeed consume more when they are old.