a bank offers an investment account with an annual interest rate of 1.14% compounded daily. brian invests…
a bank offers an investment account with an annual interest rate of 1.14% compounded daily. brian invests $3600 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. assume there are 365 days in each year. (a) assuming no withdrawals are made, how much money is in brians account after 2 years? (b) how much interest is earned on brians investment after 2 years?
Answer
Explanation:
Step1: Identify the compound - interest formula
The compound - interest formula for daily compounding 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=$3600$, $r = 0.0114$ (since $1.14%=0.0114$), $n = 365$, and $t = 2$.
Step2: Calculate the value of $(1+\frac{r}{n})$
$\frac{r}{n}=\frac{0.0114}{365}\approx0.0000312329$, and $1+\frac{r}{n}=1 + 0.0000312329=1.0000312329$.
Step3: Calculate the value of $nt$
$nt=365\times2 = 730$.
Step4: Calculate $(1+\frac{r}{n})^{nt}$
$(1.0000312329)^{730}\approx1.023177$.
Step5: Calculate the amount $A$
$A = 3600\times1.023177=$3683.44$.
Step6: Calculate the interest earned
The interest earned $I=A - P$. So, $I = 3683.44−3600=$83.44$.
Answer:
(a) $$3683.44$ (b) $$83.44$