If money is invested in a savings account earning 5.3% interest compounded daily, how many years will pass until the money doubles?
A) 13.08
B) 0.13
C) 0.00
D) 13.08.

Question

Quizplus · Accepted Answer

Using the formula for compound interest, $A = P(1 + \frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (decimal), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested for in years. To double the money, $A = 2P$. Substituting the given values and solving for $t$ when the interest rate $r = 0.053$ and it's compounded daily ($n = 365$), we use the formula for doubling time which simplifies to $t = \frac{\ln(2)}{\ln(1 + \frac{r}{n})} \times \frac{1}{n}$. Plugging in the values, we find that $t$ is approximately 13.08 years.

If Money Is Invested in a Savings Account Earning 5