question 3\nthis question has two parts. first, answer part a. then, answer part b.\npart a\nfinance rawan…

question 3\nthis question has two parts. first, answer part a. then, answer part b.\npart a\nfinance rawan deposits $13,000 into an account that pays 2.6% annual interest compounded every 6 months.\na. write a function to represent the balance a in the account after t years. round to the nearest thousandth if necessary.\npart b\nb. what will be the balance after 4 years?\nc. what will be the balance after 7.5 years?

question 3\nthis question has two parts. first, answer part a. then, answer part b.\npart a\nfinance rawan deposits $13,000 into an account that pays 2.6% annual interest compounded every 6 months.\na. write a function to represent the balance a in the account after t years. round to the nearest thousandth if necessary.\npart b\nb. what will be the balance after 4 years?\nc. what will be the balance after 7.5 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 $P = 13000$, $r=0.026$ (since $2.6%=0.026$), and $n = 2$ (compounded every 6 months). So the function is $A(t)=13000(1 +\frac{0.026}{2})^{2t}=13000(1 + 0.013)^{2t}=13000(1.013)^{2t}$.

Step2: Calculate balance after 4 years

Substitute $t = 4$ into the function $A(t)$. $A(4)=13000(1.013)^{2\times4}=13000(1.013)^{8}$. $(1.013)^{8}\approx1.108347$. $A(4)=13000\times1.108347\approx14408.511$.

Step3: Calculate balance after 7.5 years

Substitute $t = 7.5$ into the function $A(t)$. $A(7.5)=13000(1.013)^{2\times7.5}=13000(1.013)^{15}$. $(1.013)^{15}\approx1.210904$. $A(7.5)=13000\times1.210904\approx15741.752$.

Answer:

a. $A(t)=13000(1.013)^{2t}$ b. $$14408.511$ c. $$15741.752$