Interest: Compound Interest

Adam deposited a portion of his salary in a savings account in January 2005. Adam earns a 10% interest compounded annually. If Adam plans to make a withdrawal of all the money in the account in January 2010, then his withdrawal is approximately what percent of his initial deposit?

Correct. [[snippet]] __Plug In__ 100 for Adam's initial deposit (the invisible variable) in 2005. He made 10% on the first year, 10% on the second year, and so forth. What keeps changing is the total worth of his deposit, which keeps on getting bigger every year. And so, - 2005–2006: The balance is $$\$100+\$10=\$110$$. - 2006–2007: The balance is $$\$110+\$11=\$121$$. - 2007–2008: The balance is $$\$121+\$12=\$133$$. - 2008–2009: The balance is $$\$133+\$13=\$146$$. - 2009–2010: The balance is $$\$146+\$15= \$161$$. Alternatively, you can assume that the interest is _simple_ (i.e., 10% annually taken only from the original amount) instead of the successively growing balance. Thus, in 5 years, Adam will grow by $$5\cdot 10\% = 50\%$$, so he has 150% of the original amount. Since the question actually uses _compound_ interest, the actual result must be higher than 150% because of the compounded interest. Only answer choice E fits that description, so it must be the right answer.

Incorrect. [[snippet]] This is one of GMAC's traps! If you __Plugged In__ 100 for Adam's initial deposit (the invisible variable), then took 10% of it and multiplied it by 5 years, you missed the whole point. A yearly compound interest means that the interest has to be compounded every year. Each year the total worth of the deposit changes (it gets bigger).

Incorrect. [[snippet]]

Incorrect. [[snippet]] This is the percentage of interest earned by Adam. The question asks, the end worth of his deposit is approximately what percent of his initial deposit?

Incorrect. [[snippet]] This is another one of GMAC's traps! You don't add just the percentages for each year in problems about compound interest. Moreover, focus on what the question is asking.

50%

61%

100%

150%

161%