<p><a target="_blank" href="https://www.prepswift.com/quizzes/quiz/prepswift-compound-interest-ii">Compound Interest II Exercise</a></p><p><span style="color:#27ae60;">Compound Interest II</span></p>
<p>In the previous mountain entry, we discussed what would happen if you're receiving a compound annual interest rate. That means we simply have to use the number of years as our power. It's pretty straightforward. But, what if our deposit compounded twice a year? Three times a year? Four times a year? Every month? What do we do in that case?</p>
<p><strong><span style="color:#8e44ad;">Example</span></strong></p>
<p>Let's imagine we deposit $\$100$ in an account earning $8\%$ annual interest, compounding quarterly, and we leave it in there for $3$ years. Because it's compounding quarterly, our money is going to grow FOUR times a year. So let's follow this process:</p>
<p style="margin-left: 40px;"><strong>Step 1</strong>: Divide the yearly interest rate by the number of compounding periods in a year:</p>
<p>$$8\% \div 4 = 2\%$$</p>
<p style="margin-left: 40px;"><strong>Step 2</strong>: Determine how many compounding periods you have total by multiplying the number of years by the number of times it compounds each year:</p>
<p>$$3 \times 4 = 12$$</p>
<p style="margin-left: 40px;"><strong>Step 3</strong>: Set up our equation:</p>
<p>$$total = 100(1.02)^{12}$$</p>
<p>Notice that we're multiplying by $1.02$ (from step 1) rather than $1.08$. Also notice that the exponent is $12$ (from step 2) rather than $3$. </p>
<p><strong><span style="color:#8e44ad;">Additional Example</span></strong></p>
<p>John depositions $\$300$ in an account earning $12\%$ annual interest, compounding monthly, for three years. In that case, each compounding period gives us $1\%$ and each year has $12$ compounding periods. So after three years, that's $36$ compounding periods. Thus, our formula is...</p>
<p>$$total = 300(1.01)^{36}$$</p>