to help pay for new costumes for a play, a theater invests $1200 in a 42 - month cd paying 4.2% interest…

to help pay for new costumes for a play, a theater invests $1200 in a 42 - month cd paying 4.2% interest compounded monthly. determine the amount the theater will receive when it cashes in the cd after 42 months. the theater will receive $ when it cashes in the cd. (round to the nearest cent as needed.)

to help pay for new costumes for a play, a theater invests $1200 in a 42 - month cd paying 4.2% interest compounded monthly. determine the amount the theater will receive when it cashes in the cd after 42 months. the theater will receive $ when it cashes in the cd. (round to the nearest cent as needed.)

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 given values

Given $P=$1200$, $r = 4.2%=0.042$, $n = 12$ (compounded monthly), and $t=\frac{42}{12}=3.5$ years.

Step3: Substitute values into formula

$A = 1200(1+\frac{0.042}{12})^{12\times3.5}$ First, calculate the value inside the parentheses: $\frac{0.042}{12}=0.0035$, then $1 + 0.0035=1.0035$. Next, calculate the exponent: $12\times3.5 = 42$. So, $A = 1200\times(1.0035)^{42}$.

Step4: Calculate $(1.0035)^{42}$

Using a calculator, $(1.0035)^{42}\approx1.15777$.

Step5: Calculate $A$

$A = 1200\times1.15777=$1389.324$.

Answer:

$1389.32$