select the correct answer. calculate the compound amount. round to the nearest cent. p = $9000, r = 5.5%…

select the correct answer. calculate the compound amount. round to the nearest cent. p = $9000, r = 5.5%, compounded quarterly, t = 3 yrs. a $10602.60 b $10,602.61 c $10,602.62 d $10,606.21

select the correct answer. calculate the compound amount. round to the nearest cent. p = $9000, r = 5.5%, compounded quarterly, t = 3 yrs. a $10602.60 b $10,602.61 c $10,602.62 d $10,606.21

Answer

Explanation:

Step1: Identify the 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.

Step2: Convert the given values to the correct form

Given $P = 9000$, $r=0.055$ (since $5.5%=0.055$), $n = 4$ (compounded quarterly), and $t = 3$.

Step3: Substitute the values into the formula

$A=9000(1 +\frac{0.055}{4})^{4\times3}=9000(1 + 0.01375)^{12}$. First, calculate $1+0.01375=1.01375$. Then, $(1.01375)^{12}\approx1.1780689$. Multiply by the principal: $A = 9000\times1.1780689\approx10602.62$.

Answer:

C. $10,602.62$