suppose that $34,600 is invested in a certificate of deposit for 4 years at 9.3% annual interest to be…

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula when compounded $n$ times a year 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 compounded per year, and $t$ is the number of years. Here, $P=$34600$, $r = 0.093$ (since $9.3%=0.093$), $n = 365$, and $t = 4$.

Step2: Calculate the amount $A$

$A=34600(1 +\frac{0.093}{365})^{365\times4}$ First, calculate the value inside the parentheses: $\frac{0.093}{365}\approx0.000254795$. Then $1+\frac{0.093}{365}=1 + 0.000254795=1.000254795$. Next, calculate the exponent: $365\times4 = 1460$. So, $A = 34600\times(1.000254795)^{1460}$. Using a calculator, $(1.000254795)^{1460}\approx1.444777$. Then $A=34600\times1.444777\approx49989.28$.

Step3: Calculate the interest earned

The interest earned $I=A - P$. $I=49989.28-34600=$15389.28$

Answer:

$15389.28$