Jacob Neusner, The Midrash: An Introduction (Northvale: Jason Aronson, 1990) 206.
Neusner quotes Song of Songs Rabbah (sixth-seventh centuries):
"When he came and said to the Israelites, 'In this month you will be redeemed,' they said to him, 'Our lord, Moses, how are we going to be redeemed? And did not the Holy One, blessed be He, say to Abraham, "And they shall work them and torment them for four hundred years" (Genesis 15:13), and now we have in hand only two hundred and ten years!" He said to them, 'Since he wants to redeem you, he is not going to pay attention to these reckonings of yours.'"
Genesis 15:13 seems to say that the Israelites would be in Egypt for 400 years, but other passages of the Pentateuch indicate they were there for a shorter duration. Rashi (eleventh century) identifies the same problem:
Now, if you should say that they were 400 years in Egypt, [this is not so] because Kehath was one of those who descended to Egypt. If you compute the years of Kehath (133) and those of Amram (his son, 137), and the 80 years of Moses, his age when they left Egypt, you will find only 350 [years]. And you must still subtract from them all the years that Kehath lived after the birth of Amram and that Amram lived after the birth of Moses.
To calculate how long the Israelites were in Egypt, Rashi interprets Genesis 46:11 to mean that Kohath the son of Levi went down to Egypt with Jacob, when Jacob took his entire family to that country. Exodus 6 says how long Kohath and Amram lived, as well as Moses' age at the time of the Exodus, and it doesn't add up to 400 years, but to 350. And, even then, you have to subtract the overlapping years, for Kohath and Amram lived at the same time for a certain number of years, as did Amram and Moses.
Like Song of Songs Rabbah, Rashi holds that the Israelites were in Egypt for 210 years. This number is derived from the gematria of the Hebrew word redu ("go down") in Genesis 42:2, in which Jacob tells his sons to go down to Egypt for food. In gematria, each letter of the Hebrew alphabet has a numerical value, and redu adds up to 210.
Rashi attempts to reconcile the 400 years in Genesis 15:13 with the shorter duration of the Israelites' sojourn in Egypt. He points out that Genesis 15:13 says that Abraham's seed would be a sojourner (Hebrew, ger) in a land that's not theirs for 400 years. It doesn't say that the land in question would be Egypt alone. There are texts that present Abraham, Isaac, and Jacob sojourning in countries that aren't theirs (Genesis 20:1; 21:34; 47:4; Psalm 105:23). For Rashi, Genesis 15:13 predicts that Abraham's seed would sojourn in countries not their own for 400 years, which stretches from the time of Isaac's birth to the Exodus.
Song of Songs Rabbah, however, offers a different solution: God will redeem Israel when he wants to redeem her. He's not bound by the calculations of Israelites! Song of Songs Rabbah may be saying that God changed his mind about Israel being in Egypt for 400 years, so he decided to deliver her prematurely. Or perhaps it means that Israel was misinterpreting Genesis 15:13 to mean that she had to be in Egypt for 400 years, when actually it meant what Rashi later said. Notice that God calls the reckonings "yours," meaning Israel's. But didn't God speak Genesis 15:13? Yes, but the reckoning may be Israel's in the sense that she misinterpreted God's words in that verse.
But doesn't Exodus 12:40 say that "The time that the Israelites had lived in Egypt was four hundred thirty years" (NRSV)?
Mekhilta de-Rabbi Ishmael (second-eighth centuries) offers an interesting interpretation of this verse. As Rashi did years later, the Mekhilta counts the 400 years from the birth of Isaac to the Exodus, when Abraham's seed sojourned in countries that weren't theirs. But the extra 30 years that Exodus 12:40 mentions is that between God's revelation to Abraham in Genesis 15 and the birth of Isaac. From Genesis 15 to the Exodus, you have 430 years. Because Exodus 12:41 says, "At the end of four hundred thirty years, on that very day, all the companies of the LORD went out from the land of Egypt," the Mekhilta contends that exactly 430 years passed from Genesis 15 to the Exodus, not a day more, nor a day less. Consequently, God's revelation to Abraham in Genesis 15 occurred on Nisan 15, the day when Israel later left Egypt.
But "Rabbi" in Mekhilta offers what seems to be a different view: he tries to reconcile the 400 years of Genesis 15:13 with Genesis 15:16's statement that Abraham's seed would return to Canaan in the "fourth generation," which is sooner than 400 years. Rabbi says that these are two alternative possibilities: If Israel repents, God will deliver her after four generations. If not, he will deliver her after 400 years. Rabbi appears to assume that the 400 years refer to Israel's time in Egypt, not the time-span of the sojourning of Abraham's seed from Isaac to the Exodus.
Echoing Babylonian Talmud Sotah 11b, however, Rashi maintains that both the 400 years and the four generations are true: And so it was: Jacob descended to Egypt. Go forth and figure his generations: Judah, Perez, and Hezron, and Caleb the son of Hezron was one of those who entered the land (Sotah 11b). Rashi sees the 400 years as the time from Isaac's birth to the Exodus, the total duration of the "sojourn." And he also affirms that the fourth generation from Judah (who entered Egypt with Jacob) was the one that left Egypt.
But, back to Exodus 12:40, the King James translates it literally: "Now the sojourning of the children of Israel, who dwelt in Egypt, was four hundred and thirty years." One can read that to mean that the sojourn of the Israelites in various countries was 430 years, not that they were in Egypt for that whole amount of time. The rabbinic sources may assume that reading, for they don't take Exodus 12:40 to mean that the Israelites were in Egypt for 430 years. I don't think that works, though, for Isaac technically wasn't an Israelite, since Israelites are descendants of Jacob/Israel.
This post is a rough ride, I know, but hopefully I've made somewhat clear the contradictions in the biblical text, as well as the rabbinic efforts to reconcile them.