select the correct answer. calculate the compound amount. round to the nearest cent for, p = $4600, r = 5%…

select the correct answer. calculate the compound amount. round to the nearest cent for, p = $4600, r = 5%, compounded semiannually, t = 12yrs.\n(a) $8320.14\n(b) $8320.13\n(c) $8320.15\n(d) 8321.00

select the correct answer. calculate the compound amount. round to the nearest cent for, p = $4600, r = 5%, compounded semiannually, t = 12yrs.\n(a) $8320.14\n(b) $8320.13\n(c) $8320.15\n(d) 8321.00

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.

Step2: Convert values to appropriate form

Given $P = 4600$, $r=0.05$ (since $5%=0.05$), $n = 2$ (compounded semiannually), and $t = 12$.

Step3: Substitute values into formula

$A=4600(1 +\frac{0.05}{2})^{2\times12}=4600(1 + 0.025)^{24}$.

Step4: Calculate the value inside the parentheses

$1+0.025=1.025$.

Step5: Calculate the exponentiation

$(1.025)^{24}\approx1.808726$.

Step6: Calculate the compound amount

$A = 4600\times1.808726\approx8320.14$.

Answer:

A. $8320.14$