Sarah invested $38,700 in an account that paid 6.2% annual interest, compounding monthly. She left the money in this account, collecting interest for three full years. Approximately how much interest did she earn in the last month of this period?
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Wait, this is a 705-805? I got crushed by the compounding. I just took the total interest and divided by 36 and obviously that's not even an answer choice lol.
Yeah, the wording is doing a lot of work here. Once you realize it's asking for one month at the end, it gets easier, but the setup is nasty.
Key is that monthly rate is 6.2/12, and the balance at the start of month 36 is 38700*(1+r)^35. Then the last month's interest is just that times r. No need to compute the whole 3-year total.
This is the cleanest way. I wasted time finding the ending balance first, then backed into it.
Got A. The exponent thing is what makes this 700+. If it were simple interest people would get it in 30 seconds.
That off-by-one is exactly why I'm reading the comments. Thanks.
Is the monthly rate 0.062/12? I kept second-guessing whether to divide the annual rate or use an effective monthly rate. The word 'compounding monthly' usually means nominal annual divided by 12, right?
What it tests
Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.
Common trap
Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.