a bank offers an investment account with an annual interest rate of 1.18% compounded quarterly. raina…

Explanation:

Step1: Identify the 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, and $t$ is the number of years.

Step2: Convert the given values to the appropriate form

We have $P=$3500$, $r = 1.18%=0.0118$, $n = 4$ (compounded quarterly), and $t = 2$ years.

Step3: Calculate the amount $A$ in the account after 2 years

Substitute the values into the formula: [ \begin{align*} A&=3500\left(1 +\frac{0.0118}{4}\right)^{4\times2}\ &=3500\left(1+ 0.00295\right)^{8}\ &=3500\times(1.00295)^{8} \end{align*} ] Using a calculator, $(1.00295)^{8}\approx1.023877$. Then $A = 3500\times1.023877=$3583.57$.

Step4: Calculate the interest earned

The interest earned $I$ is given by $I=A - P$. So $I=3583.57−3500=$83.57$.

Answer:

(a) $$3583.57$ (b) $$83.57$