Question

a public relations writer received a promotion that came with a $7,000 salary increase. the writer wants to invest the money in a savings account with an annual interest rate of 5.4% for 10 years. how much interest would the account earn with simple interest and with monthly compounded interest? the account will earn $3,870 in simple interest and $5,012.05 in compound interest the account will earn $5,012.05 in simple interest and $3,870 in compound interest the account will earn $3,780 in simple interest and $4,997.51 in compound interest the account will earn $4,997.51 in simple interest and $3,780 in compound interest

Explanation:

Step1: Calculate simple - interest

The simple - interest formula is $I = Prt$, where $P$ is the principal amount, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $P=\$7000$, $r = 0.054$, and $t = 10$.
$I=Prt=7000\times0.054\times10 = 7000\times0.54=\$3780$

Step2: Calculate compound - interest

The compound - interest formula for monthly compounding 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. Here, $P = 7000$, $r=0.054$, $n = 12$, and $t = 10$.
First, calculate the value inside the parentheses: $1+\frac{r}{n}=1+\frac{0.054}{12}=1 + 0.0045=1.0045$.
Then, calculate the exponent: $nt=12\times10 = 120$.
So, $A = 7000\times(1.0045)^{120}$.
Using a calculator, $(1.0045)^{120}\approx1.71393$.
$A=7000\times1.71393=\$11997.51$.
The compound interest $I=A - P=11997.51−7000=\$4997.51$

Answer:

The account will earn $3,780 in simple interest and $4,997.51 in compound interest. So the correct option is: The account will earn $3,780 in simple interest and $4,997.51 in compound interest.