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		<title>GRE Interest Problems</title>
		<link>https://www.manhattanprep.com/gre/blog/gre-interest-problems/</link>
		
		<dc:creator><![CDATA[Neil Thornton]]></dc:creator>
		<pubDate>Wed, 07 Jun 2017 16:52:01 +0000</pubDate>
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		<category><![CDATA[GRE Interest Problems]]></category>
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					<description><![CDATA[<p>You can attend the first session of any of our online or in-person GRE courses absolutely free. Ready to take the plunge? Check out our upcoming courses here. Interesting Interest Deposit money into a savings account and you will earn interest. Rack up a bunch of charges on your credit card, and you’re going to [&#8230;]</p>
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										<content:encoded><![CDATA[<p><img decoding="async" fetchpriority="high" class="alignnone size-full wp-image-10428" src="//cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-interest-problems-neil-thornton.png" alt="Manhattan Prep GRE Blog - GRE Interest Problems by Neil Thornton" width="1200" height="628" srcset="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-interest-problems-neil-thornton.png 1200w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-interest-problems-neil-thornton-300x157.png 300w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-interest-problems-neil-thornton-768x402.png 768w, https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/gre-interest-problems-neil-thornton-1024x536.png 1024w" sizes="(max-width: 1200px) 100vw, 1200px" /></p>
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<h4><b><i></i></b><b>Interesting Interest</b></h4>
<p><span style="font-weight: 400;">Deposit money into a savings account and you will earn interest. Rack up a bunch of charges on your credit card, and you’re going to be charged interest. In the real world, the bank takes care of calculating interest for you, but if the word “interest” shows up on the GRE, you’re going to need to know how to calculate it yourself. </span><span id="more-10404"></span></p>
<h4><b>Simple Interest</b></h4>
<p><span style="font-weight: 400;">Simple interest is just that. Simple. Take that percent of the principal and tack it on.</span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Alice invested $1000 at 8% simple annual interest. How much is the investment worth after one year?</span></i></p>
<p><span style="font-weight: 400;">Some terms you should know:</span></p>
<p><b>The principal:</b><span style="font-weight: 400;"> The amount originally deposited. With a debt, it’s the amount you borrowed initially. </span></p>
<p><b>The interest rate:</b><span style="font-weight: 400;"> Usually “annual,” the interest rate is the percentage of the principal earned over a period of time.</span></p>
<p><span style="font-weight: 400;">Calculate 8% of that $1000 principal. (8/100 * 1000 = 80). Over the year Alice earned $80, so at the end of the year, the account is worth $1080. Done.</span></p>
<p><span style="font-weight: 400;">You could use your calculator, too (though it may be a waste of time). Convert the interest rate into a decimal (.08) and add 1 (1.08). [That 1 represents the original principal.] Multiply that principal by 1.08. </span></p>
<p style="padding-left: 30px;"><span style="font-weight: 400;">$1000 x 1.08 = 1080</span></p>
<p><span style="font-weight: 400;">With simple interest, the percent is always based on the </span><i><span style="font-weight: 400;">original</span></i><span style="font-weight: 400;"> amount, so for multiple years, Alice will continue to earn $80 every year. Over 5 years, Alice would earn $400 simple interest. </span></p>
<h4><b>Compound Interest</b></h4>
<p><span style="font-weight: 400;">“Compound interest” means that every so often, the bank will add something to the principal (or the credit card company will add something to your debt). Each time after that, the bank will calculate the next interest payment based on the NEW amount of money in the principal. Over a short amount of time, compounding will add only a smidge to the principal. Over a long period of time, compounding can add a great deal to the principal (as I learned the hard way after college).  </span></p>
<p><span style="font-weight: 400;">Every so often you’ll see confusing statements such as “8% annual interest compounded semi-annually” or “12% annual interest compounded quarterly.”</span></p>
<p><span style="font-weight: 400;">“8% annual interest compounded semi-annually” means the bank will divide that 8% over the year by the number of “periods” in that year. Semi-annually means twice a year, so the bank will divide that 8% by 2. You get 4% every six months. </span></p>
<p><span style="font-weight: 400;">“12% annual interest compounded quarterly” means you get 12%/4, or 3% four times a year (every 3 months). </span></p>
<p><span style="font-weight: 400;">“24% annual interest compounded monthly” mean you get 2% 12 times a year (every month).</span></p>
<h4><b>Technique 1: Brute Force/Be the Bank</b></h4>
<p><span style="font-weight: 400;">The most effective and efficient way to work out compound interest on the GRE is to pretend to be the bank. Just work each payment out, piece by piece, one “period” at a time. Consider the following question:</span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Alice invested $1000 at 8% annual interest compounded every 6 months (semi-annually). How much is the investment worth after one year?</span></i></p>
<p><span style="font-weight: 400;">Look at the annual interest, and divide it by the number of periods each year. 8% divided by 2 periods a year = 4% every period. Then get to work.</span></p>
<p><span style="font-weight: 400;">Alice puts $1000 into the account, where it sits for 6 months. After 6 months, Alice is going to get some interest. Since it’s halfway through the year, she’ll get half of that 8%. </span></p>
<p><span style="font-weight: 400;">4% of $1000 is $40, which will be added to her account. She now has $1040.</span></p>
<p><span style="font-weight: 400;">At the end of the year, she’ll get the other 4%, but since the interest is </span><i><span style="font-weight: 400;">compounded</span></i><span style="font-weight: 400;">, she’ll get 4% of the 1040 that’s in her account now!</span></p>
<p><span style="font-weight: 400;">4% of 1040 is 41.60, which will be added to her account, leaving her with $1081.60. </span></p>
<h4><b>Technique 2: Simple Plus a Smidge</b></h4>
<p><span style="font-weight: 400;">Imagine the same question, but it’s multiple choice this time:</span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Alice invested $1000 at 8% annual interest compounded every 6 months (semi-annually). How much is the investment worth after one year?</span></i></p>
<p style="padding-left: 30px;"><em><span style="font-weight: 400;">(A) $1040<br />
</span><span style="font-weight: 400;">(B) $1080<br />
</span><span style="font-weight: 400;">(C) $1081.60<br />
</span><span style="font-weight: 400;">(D) $1160<br />
</span><span style="font-weight: 400;">(E) $1166.40</span></em></p>
<p><span style="font-weight: 400;">If you know that “compounding” adds a tiny bit of interest over a short amount of time, you can get THIS one very very quickly.</span></p>
<p><span style="font-weight: 400;">All you do is figure out the simple interest over the year, and pick the answer that’s a teeny tiny bit more than that. </span></p>
<p><span style="font-weight: 400;">If it were simple interest, 8% annual interest would be $80, leaving $1080 in the account. But since the interest is compounded, the only possible answer is the one a tiny bit more than that: (C) 1081.60. </span></p>
<h4><b>Technique 3: The Compound Interest Formula</b></h4>
<p><span style="font-weight: 400;">But what if the answers look funny? </span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Amy invested $5000 at 12% annual interest compounded quarterly. How much is her investment worth after 5 years?</span></i></p>
<p style="padding-left: 30px;"><img decoding="async" class="alignnone size-full wp-image-10405" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/nt-12-image-1.png" alt="Manhattan Prep GRE Blog - GRE Interest Problems by Neil Thornton" width="148" height="101" /></p>
<p><span style="font-weight: 400;">This is one of the few cases in which it’s important to know the “compound interest formula.” The </span><a id="bloglink" href="https://www.manhattanprep.com/gre/store/official-guides-for-gre/official-guide-gre-revised-general-test/" target="_blank" rel="noopener noreferrer"><span style="font-weight: 400;">Official Guide to the GRE</span></a><span style="font-weight: 400;"> gives us a formula that is nearly incomprehensible and very easy to get messed up:</span></p>
<p><img decoding="async" class="alignnone size-full wp-image-10406 aligncenter" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/nt-12-image-2.png" alt="Manhattan Prep GRE Blog - GRE Interest Problems by Neil Thornton" width="129" height="52" /></p>
<p><span style="font-weight: 400;">What? Huh? Forget it. </span></p>
<p><span style="font-weight: 400;">Let’s break this down and make this MUCH easier. Ask yourself a few questions:</span></p>
<p><span style="font-weight: 400;">What’s the interest rate every period? Convert that to a decimal. </span></p>
<p><span style="font-weight: 400;">How many periods? How many times is money going into the account?</span></p>
<p><span style="font-weight: 400;">In Amy’s case, “</span><i><span style="font-weight: 400;">12% annual interest compounded quarterly” </span></i><span style="font-weight: 400;">means she’s getting 12/4, or 3% every period. As a decimal, that’s .03.</span></p>
<p><i><span style="font-weight: 400;">“Compounded quarterly</span></i><span style="font-weight: 400;">” over 5 years means she’ll be getting money 4 x 5 = 20 times.</span></p>
<p><span style="font-weight: 400;">A simplified version of the formula is this, <em>V</em> = value of the investment: </span></p>
<p><img decoding="async" loading="lazy" class="alignnone size-full wp-image-10407 aligncenter" src="https://cdn2.manhattanprep.com/gre/wp-content/uploads/sites/19/2017/05/nt-12-image-3.png" alt="Manhattan Prep GRE Blog - GRE Interest Problems by Neil Thornton" width="295" height="42" /></p>
<p><span style="font-weight: 400;">We already figured out that her </span><i><span style="font-weight: 400;">rate per period</span></i><span style="font-weight: 400;"> is .03, with 20 periods. Therefore, the value of Amy’s investment after 5 years will be 5000(1.03)<sup>20</sup></span><span style="font-weight: 400;">. Answer choice (E).</span></p>
<p><span style="font-weight: 400;">Back to our original problem:</span></p>
<p style="padding-left: 30px;"><i><span style="font-weight: 400;">Alice invested $1000 at 8% annual interest compounded every 6 months (semi-annually). How much is the investment worth after one year?</span></i></p>
<p style="padding-left: 30px;"><em><span style="font-weight: 400;">(A) $1040<br />
</span><span style="font-weight: 400;">(B) $1080<br />
</span><span style="font-weight: 400;">(C) $1081.60<br />
</span><span style="font-weight: 400;">(D) $1160<br />
</span><span style="font-weight: 400;">(E) $1166.40</span></em></p>
<p><span style="font-weight: 400;">The formula would be 1000(1.04)²</span><span style="font-weight: 400;"> = 1081.60.</span></p>
<p><span style="font-weight: 400;">Keep in mind, the GRE calculator does NOT do exponents, so you’d have to key in 1000 x 1.04 x 1.04, which may be tedious and error-prone. </span></p>
<h4><b>In Sum</b></h4>
<p><span style="font-weight: 400;">When you get an interest problem on the GRE, ask yourself a few questions:</span></p>
<p><span style="font-weight: 400;">Is this simple or compound?</span></p>
<p><span style="font-weight: 400;">If it’s compound, can I ballpark the answer with “Simple plus a smidge?”</span></p>
<p><span style="font-weight: 400;">If not, would it be better to use brute force (be the bank) or to apply the compound interest formula (if the answers look like the interest formula)?</span></p>
<p><span style="font-weight: 400;">We have tons of examples in the </span><a href="https://www.manhattanprep.com/gre/store/strategy-guides/5-pound-book-gre-practice-problems/" target="_blank" rel="noopener noreferrer"><i><span style="font-weight: 400;">Manhattan Prep 5-lb Book of GRE Practice Problems</span></i></a><span style="font-weight: 400;">, so get to work locking in those skills! ?</span></p>
<hr />
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<p><b><i><a href="https://www.manhattanprep.com/gre/mondays-with-neil/?utm_source=manhattanprep.com%2Fgre%2Fblog&#038;utm_medium=blog&#038;utm_content=GRE%20Blog%20Mondays%20with%20Neil%20Plug&#038;utm_campaign=GRE%20Blog%20Product%20Push"><img decoding="async" loading="lazy" class="alignleft wp-image-9096 size-thumbnail" src="https://d27gmszdzgfpo3.cloudfront.net/gre/wp-content/uploads/sites/19/2016/06/neil-thornton-150x150.png" alt="Neil Thornton Instructor Headshot" width="150" height="150" /></a></i></b><i><em><strong>When not onstage telling jokes, <a id="bloglink" href="https://www.manhattanprep.com/instructors/neil-thornton/" target="_blank" rel="noopener noreferrer">Neil Thornton</a> loves teaching you to beat the GRE and GMAT.</strong> Since 1991, he’s coached thousands of students through the GRE, GMAT, LSAT, MCAT, and SAT, and trained instructors all over the United States. He scored 780 on the GMAT, a perfect 170Q/170V on the GRE, and a 99th-percentile score on the LSAT. <a id="bloglink" href="https://www.manhattanprep.com/gre/classes/#instructor/35" target="_blank" rel="noopener noreferrer">Check out Neil’s upcoming GRE course offerings here</a> or join him for a free online study session twice monthly in <a id="bloglink" href="https://www.manhattanprep.com/gre/mondays-with-neil/" target="_blank" rel="noopener noreferrer">Mondays with Neil</a>.</em></i></p>
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