oliver would like to buy some new furniture for his home. he decides to buy the furniture on credit with…

Explanation:

Step1: Identify the compound - interest formula

The compound - interest formula is $A = P(1+\frac{r}{n})^{nt}$, where $A$ is the amount of money accumulated after $n$ years, including interest, $P$ is the principal amount (the initial amount of money), $r$ is the annual interest rate (in decimal form), $n$ is the number of times that interest is compounded per year, and $t$ is the time the money is invested or borrowed for in years.

Step2: Convert the given values to the appropriate form

The principal amount $P=$5400$, the annual interest rate $r = 9.5%=0.095$, the number of times compounded per year $n = 4$ (since it is compounded quarterly), and the time $t = 7$ years.

Step3: Substitute the values into the formula

$A=5400(1 +\frac{0.095}{4})^{4\times7}$. First, calculate the value inside the parentheses: $\frac{0.095}{4}=0.02375$, and $1+\frac{0.095}{4}=1 + 0.02375=1.02375$. Then, calculate the exponent: $4\times7 = 28$. So, $A = 5400\times(1.02375)^{28}$.

Step4: Calculate $(1.02375)^{28}$

Using a calculator, $(1.02375)^{28}\approx1.95797$.

Step5: Calculate the final amount $A$

$A=5400\times1.95797 = 10573.038\approx10573.04$.

Answer:

$10573.04$