Compound interest implies that each month the account balance grows by a fixed percentage (a constant multiplier). For instance if the interest is 10%, each month the balance will be multiplied by 1.10. Let's call this multiplier g. The following table shows the account balance at the start of each month
Jan 2003: $10,000
Feb 2003: 10,000g
Mar 2003: 10,000g^2
...
So the balance at any point can be expressed as 10,000 * g^k where k is the amount of time (in months) that has expired.
Since knowing the monthly percentage interest is enough to find the annual percentage interest, we can rephrase the question to ask: "What is g?"
Statement 1:
Interest accrued from start of Nov to the start of Dec 2003 was $61.83
The interest earned in a month is just the difference between balances at the beginning of the month and the end of the month. At the start of Nov 2003, the balance is 10,000 * g^10. At the end of that month, it is 10,000 * g^10 * g. We can think of this logically. As g gets bigger, the difference between 10,000g^10 and 10,000g^11 always gets bigger (we know g is positive since the account accrues interest). This means that there must be a unique value of g for which the difference between the two balances is exactly 61.83. since we can demonstrate that there is a unique solution (even if we don't know how to find it), we can be confident that there is sufficiency.
Algebraically, the relevant equation is 10,000g^11 - 10,000g^10 = 61.83
Statement 1 is SUFFICIENT.
Statement 2:
Again, a logical approach is simplest. Given that we know the total duration of the investment, and since every incremental increase in g will result in an always greater total interest, there must be a unique value of g for which the total interest accumulated is $4,176.25. This means that logically, we have enough data to find g because we've demonstrated that there is a unique value of g that will fit the statement.
Algebraically, it is easy to build an equation. There are a total of 66 months, so the total interest (difference between final balance and initial investment) can be written as: 10,000g^66 - 10,000 = 4,176.25
Statement 2 is SUFFICIENT.
[spoiler]
The answer is D[/spoiler]
