Sorry, I cannot agree with the independence assumption. Fertility in women, even without contraception is a function of age, such that, without contraception the
Chances of getting pregnant without IVF (in vitro fertilization)
Starting at about age 32, a woman’s chances of conceiving decrease gradually but significantly.
From age 35, the fertility decline speeds up.
By age 40, fertility has fallen by half.
At 30, the chance of conceiving each month is about 20%. At 40 it’s around 5%.
Note (mine) after age ~49 menopause occurs and when it does, women are infertile.
The rate of pregnancy is also a function of frequency of intercourse, which also changes with age:
About 5% of single women between the ages of 18 and 24 had sex 4 or more times per week, but 24% of married women did.
Like the men, just under half of the women between the ages of 25 and 59 had sex a few times per month to weekly, more than their single and partnered peers.
Sexual frequency did decrease with age for women, although almost a quarter of partnered women over age 70 had sex more than 4 times a week.
Relative time of ovulation, intercourse, and female age:
Finally, to consider the effectiveness of contraception on an annualized basis, one must consider not only decreasing fertility and variable but generally somewhat decreasing sexual frequency with age, but likely also myriad other factors. For example, the percentage of women who are postpartum increases with age, and postpartal women may have a different contraceptive usage effectiveness than the nulliparous, age of the partner at time of intercourse relative to ovulation, see image:
timing of intercourse relative to ovulation, having a huge impact on fertility, also reflects on the likelihood of pregnancy even when other factors, like contraception is considered. Thus, a woman who relies on the rhythm method, as well as one or more other methods of contraception, i.e., a woman who both knows her body functions, and uses that knowledge (and as knowledge is acquired) may eventually do an increasingly effective job of avoiding pregnancy, such that there is essentially no chance for independence of fertility with elapsed age.