Mary deposited a sum of $x$ dollars into an account that earned 4% annual interest compounded annually. One year later she deposited an additional $x$ dollars in the account. There were no other transactions. If the account showed $y$ dollars at the end of the two years, which of the following expresses $x$ in terms of $y$ ?

Correct answer marked below

y/2.04

y/1.12

y/2.2

y/(1.04\times 2.04)

Correct

y/((1.04)^2\times 2.04)

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Comments

AddyontherocksJul 13

This one got me because I forgot the first deposit also keeps growing during the second year. Took me way longer than it should have.

TommasoJul 22

Same here, the timeline is sneaky. I had to literally write out year by year.

CiroJul 23

Yeah once you list what's in the account at the end of each year it gets way clearer.

RodanthiMay 2

Why is (B) wrong? I keep getting y/1.12 when I try to shortcut it.

ArjunMay 8

Because the first x gets compounded twice, not just once. The shortcut treats both deposits the same.

DevanganaMay 4

Think about it: the first deposit earns interest for 2 years, the second only for 1. They're not equal.

UnwuonJun 1

Tricky but fair. The trap choices are all close to each other so you can't guess your way out.

DhevaJun 2

Right, you actually have to set up the equation properly. Good question.

Leonardo9h ago

Thanks, this was helpful practice.

What this question tests

Your ability to compute percentage change, percentage of a whole, and to work backwards from a final value.

Treating successive percentage changes as additive — a 10% rise then a 10% fall is not back to the start.