Solve the problem.
-Use your graphing calculator to find how long it will take for $8500 invested at 4.825% per year compounded daily to triple in value. Find the answer to the nearest year. Use 365 days for a year.
A) 0 yr
B) 23 yr
C) 3,033,623 yr
D) 30,534 yr

Question

Quizplus · Accepted Answer

To find how long it will take for an investment to triple in value, we can use 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. In this case, we want the final amount $A$ to be triple the principal $P$, so $A = 3P = 3 \times 8500$, $r = 4.825\% = 0.04825$, and $n = 365$ (since the interest is compounded daily). We solve for $t$. Rearranging the formula and solving for $t$ gives us the number of years required to triple the investment. Using a graphing calculator to solve for $t$ gives a result close to 23 years.

Solve the Problem. -Use Your Graphing Calculator to Find How Long It Will