adam is going to invest in an account paying an interest rate of 4.2% compounded quarterly. how much would…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the final amount, $P$ is the principal amount (initial investment), $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years. We are given $A = 6200$, $r=0.042$ (since $4.2%=0.042$), $n = 4$ (compounded quarterly), and $t = 19$. We need to solve for $P$.

Step2: Rearrange the formula for $P$

Starting with $A = P(1+\frac{r}{n})^{nt}$, we can solve for $P$ by dividing both sides of the equation by $(1+\frac{r}{n})^{nt}$. So $P=\frac{A}{(1 +\frac{r}{n})^{nt}}$.

Step3: Substitute the given values

Substitute $A = 6200$, $r = 0.042$, $n = 4$, and $t = 19$ into the formula for $P$: First, calculate the exponent part: $\frac{r}{n}=\frac{0.042}{4}=0.0105$ and $nt=4\times19 = 76$. Then, $(1+\frac{r}{n})^{nt}=(1 + 0.0105)^{76}$. Using a calculator, $(1.0105)^{76}\approx2.1977$. Now, $P=\frac{6200}{(1.0105)^{76}}=\frac{6200}{2.1977}\approx2821$.

Answer:

$2821$