a bank offers an investment account with an annual interest rate of 1.18% compounded quarterly. raina…
a bank offers an investment account with an annual interest rate of 1.18% compounded quarterly. raina invests $3500 into the account for 2 years. answer the questions below. do not round any intermediate computations, and round your final answers to the nearest cent. if necessary, refer to the list of financial formulas. (a) assuming no withdrawals are made, how much money is in rainas account after 2 years? (b) how much interest is earned on rainas investment after 2 years?
Answer
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, and $t$ is the number of years. Here, $P = 3500$, $r=0.0118$ (since $1.18%=0.0118$), $n = 4$ (compounded quarterly), and $t = 2$.
Step2: Calculate the amount in the account
Substitute the values into the formula: [ \begin{align*} A&=3500(1 +\frac{0.0118}{4})^{4\times2}\ &=3500(1+ 0.00295)^{8}\ &=3500\times(1.00295)^{8} \end{align*} ] Using a calculator, $(1.00295)^{8}\approx1.02387$. Then $A = 3500\times1.02387=3583.545\approx3583.55$.
Step3: Calculate the interest earned
The interest earned $I$ is given by $I=A - P$. So, $I=3583.55 - 3500=83.55$.
Answer:
(a) $$3583.55$ (b) $$83.55$