Test 8 Section 4 #23

I think the easiest way to get this one is to plug in some numbers. We know that every 4 quarters is a year, so the correct answer will be the one that gives us the same result for 1 year as 4 quarters, 2 years as 8 quarters, 3 years as 12 quarters, etc.

At 1 year, the original equation works out thusly:


Which answer choice(s) result in the same expression when q = 4? Only choice A does:


If you’re concerned that another one might also work, just check with your calculator!

    \begin{align*}1800(1.02)^1&=1836\\1800(1.02)^\frac{4}{4}&=1836\\1800(1.02)^{4(4)}&\approx 2471\\1800(1.005)^{4(4)}&\approx 1950\\1800(1.082)^4&\approx 2467\end{align*}

Sure enough, only choice A gives you the same result after 4 quarters that the original equation gives you for 1 year.