jessica received a $1700 bonus. she decided to invest it in a 3 - year certificate of deposit (cd) with an…
jessica received a $1700 bonus. she decided to invest it in a 3 - year certificate of deposit (cd) with an annual interest rate of 1.25% compounded daily. 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. assume there are 365 days in each year. (a) assuming no withdrawals are made, how much money is in jessicas account after 3 years? (b) how much interest is earned on jessicas investment after 3 years?
Answer
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=$1700$, $r = 0.0125$ (since $1.25%=0.0125$), $n = 365$, and $t = 3$.
Step2: Calculate the amount $A$
$A=1700(1 +\frac{0.0125}{365})^{365\times3}$ $A=1700(1+\frac{0.0125}{365})^{1095}$ First, calculate $\frac{0.0125}{365}\approx0.0000342466$. Then $1+\frac{0.0125}{365}=1.0000342466$. $(1.0000342466)^{1095}\approx1.038127$. $A = 1700\times1.038127=$1764.82$.
Step3: Calculate the interest earned
The interest earned $I$ is given by $I=A - P$. $I=1764.82-1700=$64.82$.
Answer:
(a) $$1764.82$ (b) $$64.82$