find the accumulated value of an investment of $10,000 for 4 years at an interest rate of 1.45% if the money…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, $t$ is the number of years, and $A$ is the accumulated amount. For continuous compounding, the formula is $A = Pe^{rt}$. Given $P=$10000$, $r = 0.0145$, and $t = 4$.

Step2: Calculate for quarterly compounding ($n = 4$)

Substitute $P = 10000$, $r=0.0145$, $n = 4$, and $t = 4$ into the compound - interest formula $A = P(1+\frac{r}{n})^{nt}$. $A=10000(1 +\frac{0.0145}{4})^{4\times4}$ First, calculate the value inside the parentheses: $\frac{0.0145}{4}=0.003625$, then $1+\frac{0.0145}{4}=1.003625$. Next, calculate the exponent: $4\times4 = 16$. So, $A = 10000\times(1.003625)^{16}$. $(1.003625)^{16}\approx1.05967$. $A = 10000\times1.05967=$10596.70$

Answer:

$10596.70$