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?
__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
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.
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).
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?
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.