blake is going to invest in an account paying an interest rate of 5.7% compounded daily. how much would…

Answer:

$30,700$

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. Given $A=$76000$, $r = 0.057$ (since $5.7%=0.057$), $n = 365$ (compounded daily), and $t = 17$ years. We need to solve for $P$.

Step2: Rearrange the formula for $P$

$P=\frac{A}{(1 +\frac{r}{n})^{nt}}$. Substitute the values: $\frac{r}{n}=\frac{0.057}{365}\approx0.000156164$, and $nt=365\times17 = 6205$. Then $(1+\frac{r}{n})^{nt}=(1 + 0.000156164)^{6205}$. Using a calculator, $(1 + 0.000156164)^{6205}\approx2.4755$.

Step3: Calculate $P$

$P=\frac{76000}{2.4755}\approx30699.1$. Rounding to the nearest hundred dollars, $P\approx30700$.