question 2\nthis question has two parts. firs...
question 2\nthis question has two parts. first, answer part a. then, answer part b.\npart a\nfinance corey deposits $2100 into an account that pays 4.2% annual interest compounded monthly.\na. write a function to represent the balance a in the account after t years.\npart b\nb. what will be the balance after 5 years?\nc. what will be the balance after 10 years?
Answer
# Explanation:
## Step1: Recall 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.
Given $P = 2100$, $r=0.042$ (since $4.2\%=0.042$), and $n = 12$ (compounded monthly).
The function for the balance $A$ in the account after $t$ years is $A(t)=2100(1 +\frac{0.042}{12})^{12t}=2100(1 + 0.0035)^{12t}=2100(1.0035)^{12t}$.
## Step2: Calculate balance after 5 years
Substitute $t = 5$ into the function $A(t)$.
$A(5)=2100(1.0035)^{12\times5}=2100(1.0035)^{60}$.
$(1.0035)^{60}\approx1.232997$.
$A(5)=2100\times1.232997\approx2589.29$.
## Step3: Calculate balance after 10 years
Substitute $t = 10$ into the function $A(t)$.
$A(10)=2100(1.0035)^{12\times10}=2100(1.0035)^{120}$.
$(1.0035)^{120}\approx1.521997$.
$A(10)=2100\times1.521997\approx3196.19$.
# Answer:
Part A: $A(t)=2100(1.0035)^{12t}$
Part B:
b. $\$2589.29$
c. $\$3196.19$