Solve the problem.
-Find how long it will take for $8600 invested at 9.325% per year compounded daily to triple in value. Find the answer to the nearest year.
A) 1,569,773 years
B) 15,895 years
C) 0 years
D) 12 years

Question

Quizplus · Accepted Answer

To find the time it takes for an investment to triple in value with daily compounding interest, we use the formula $A = P(1 + \frac{r}{n})^{nt}$, 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 triple the investment, $A = 3P$. Given $P = \$8600$, $r = 9.325\% = 0.09325$, and $n = 365$ (since the interest is compounded daily), we solve for $t$:$$3P = P(1 + \frac{0.09325}{365})^{365t}$$$$3 = (1 + \frac{0.09325}{365})^{365t}$$Taking the natural logarithm of both sides:$$\ln(3) = 365t \ln(1 + \frac{0.09325}{365})$$$$t = \frac{\ln(3)}{365 \ln(1 + \frac{0.09325}{365})}$$Calculating this gives a value close to 12 years, hence the investment will take approximately 12 years to triple in value.

Solve the Problem. -Find How Long It Will Take for $8600 Invested at $8600