You can use the compound interest formula (if you have it memorized) to solve, but glance at the answers. They're decently far apart. Plus, the question asks for an approximate answer. Estimate!
Dayo's interest rate is 8% annually, but compounded quarterly. In other words, each quarter, Dayo will earn 2% interest (and that adds up to the total 8% over the course of four quarters, or a full year).
The problem asks about the first two quarters, so Dayo will earn 2% in each of those quarters. But how can you figure out what the starting investment amount was without writing a complicated equation?
This problem is asking you to solve for the starting point—in the real world, the first thing you'd figure out is how much you were going to invest. When the problem asks you to solve for the "real world" starting point, then that starting point is somewhere in the answer choices. So Work Backwards! Try the answers to find the one that works. (And estimate—quick and dirty for the win.)
This problem tosses in a twist: It asks for the minimum that Dayo will have to invest. In other words, more than one answer may result in Dayo earning more than $100 in interest, but only one of those answers will be the minimum value. In order to minimize (no pun intended) the number of answers you have to try, start somewhere in the middle with a number that looks easy to work with.
(C) $2,000
Dayo earns 2% of $2,000 in the first quarter. Find 1% of 2,000 and double it: $2,000 becomes $20 becomes $40. So Dayo earns $40 in the first quarter and now has a total of $2,040 in the bank. In the second quarter, Dayo again earns 2%, but the new starting number is $2,040 rather than $2,000. How does that affect the amount of interest Dayo earns?
It increases it very slightly. Dayo earns $40 plus a little bit in the second quarter, for a total of $80 and a little bit. The problem wants Dayo to earn at least $100, so this isn't enough. Eliminate answers (A), (B), and (C).
Since the problem asks for the minimum, try the next higher value. [If you tried answer (E) and it worked, it might still be the case that (D) is the correct answer, since (D) might represent the minimum.]
(D) $2,500
Dayo earns 2% in the first quarter: 1% of 2,500 is 25, so 2% is 50. In the second quarter, Dayo will earn $50 plus a little bit. Total interest earned is 50 + 50 + a little bit, which is more than $100. Since answer (E) is greater, it will work too, but it can't be the minimum, since (D) works. Eliminate (E).
The correct answer is (D).
Tip: When working backwards from the answer choices, take a moment to think about where you want to start, based on the details of the problem. If you do, most of the time, you won't have to try more than two answer choices. In this case, if (D) hadn't worked, then you'd have known that (E) was the correct answer without having to try it.
