Question

Your grandmother deposits five hundred dollars into a savings account for you to access when you get older. The account carries a four percent simple annual interest rate. If you want to let the balance grow until it is worth seven hundred dollars, how many years must you wait?

Answer 1

How much interest will you earn per year?

Answer 2

\[Interest = Principle \cdot Rate ^ {Time} \]

We want to find time. Our rate is 100% + 4% = 104% = 1.04

\[$700 = $500 * 1.04 ^ x \]
\[\frac{700}{500} = 1.04^x \]
\[ln\left(\frac{700}{500}\right) = x \cdot ln(1.04) \]
\[x = \frac{ln\left(\frac{700}{500}\right)}{ ln(1.04)} \]
\[ x = 8.57 \]

So it's going to take 9 years since interest won't collect until a year finishes.