question 1 this question has two parts. first...
question 1 this question has two parts. first, answer part a. then, answer part b. part a savings tricia deposits $1500 into a savings account that pays 1.2% annual interest compounded quarterly. a. write a function to represent the balance a in the account after t years. part b b. what will be the balance after 3 years? c. what will be the balance after 6 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.
Given $P = 1500$, $r=0.012$ (since $1.2\%=0.012$), and $n = 4$ (compounded quarterly).
## Step2: Write the function for Part A
Substitute the values into the formula: $A(t)=1500(1 +\frac{0.012}{4})^{4t}=1500(1 + 0.003)^{4t}=1500(1.003)^{4t}$.
## Step3: Calculate balance for Part B ($t = 3$)
Substitute $t = 3$ into the function $A(t)$:
$A(3)=1500(1.003)^{4\times3}=1500(1.003)^{12}$.
$(1.003)^{12}\approx1.036609$.
$A(3)=1500\times1.036609 = 1554.9135\approx1554.91$.
## Step4: Calculate balance for Part C ($t = 6$)
Substitute $t = 6$ into the function $A(t)$:
$A(6)=1500(1.003)^{4\times6}=1500(1.003)^{24}$.
$(1.003)^{24}\approx1.074425$.
$A(6)=1500\times1.074425=1611.6375\approx1611.64$.
# Answer:
Part A: $A(t)=1500(1.003)^{4t}$
Part B: $1554.91$
Part C: $1611.64$