susan received a $1700 bonus. she decided to invest it in a 3 - year certificate of deposit (cd) with an…
susan received a $1700 bonus. she decided to invest it in a 3 - year certificate of deposit (cd) with an annual interest rate of 1.34% compounded quarterly. 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 susans account after 3 years? (b) how much interest is earned on susans investment after 3 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=$1700$, $r = 0.0134$ (since $1.34%=0.0134$), $n = 4$ (compounded quarterly), and $t = 3$.
Step2: Calculate the amount $A$
Substitute the values into the formula: [ \begin{align*} A&=1700\left(1 +\frac{0.0134}{4}\right)^{4\times3}\ &=1700\left(1+ 0.00335\right)^{12}\ &=1700\times(1.00335)^{12} \end{align*} ] Using a calculator, $(1.00335)^{12}\approx1.040677$. Then $A = 1700\times1.040677=$1769.1509\approx$1769.15$.
Step3: Calculate the interest earned
The interest earned $I$ is given by $I=A - P$. $I=1769.15 - 1700=$69.15$.
Answer:
(a) $$1769.15$ (b) $$69.15$