how many years will it take to triple an investment of $5,000 at an interest rate of 4% compounded annually…

Answer:

C. 29

Explanation:

Step1: Recall compound - interest formula

The compound - interest formula is $A = P(1 + r)^t$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the number of years. We want to triple the investment, so $A = 3P$. Given $P=5000$ and $r = 0.04$. Substituting into the formula, we get $3P=P(1 + 0.04)^t$.

Step2: Simplify the equation

Since $P\neq0$, we can divide both sides of the equation $3P=P(1 + 0.04)^t$ by $P$. The equation simplifies to $3=(1.04)^t$.

Step3: Take the natural logarithm of both sides

$\ln(3)=\ln(1.04^t)$. Using the property of logarithms $\ln(a^b)=b\ln(a)$, we have $\ln(3)=t\ln(1.04)$.

Step4: Solve for $t$

$t=\frac{\ln(3)}{\ln(1.04)}$. We know that $\ln(3)\approx1.0986$ and $\ln(1.04)\approx0.0392$. Then $t=\frac{1.0986}{0.0392}\approx28.0255\approx29$.