a newscaster earns $27,800 and wants to invest 10% of his/her salary to save for retirement in 24 years. if…

Explanation:

Step1: Calculate annual savings

The newscaster earns $27800$ and saves 10% of it. So the annual - savings is $0.1\times27800$. $0.1\times27800 = 2780$

Step2: Calculate monthly deposit

Since there are 12 months in a year, the monthly deposit is $\frac{2780}{12}$. $\frac{2780}{12}\approx231.67$

Step3: Use the future - value of an ordinary annuity formula

The formula for the future - value of an ordinary annuity is $F = A\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$, where $A$ is the monthly payment, $r$ is the annual interest rate (as a decimal), $n$ is the number of times compounded per year, and $t$ is the number of years. Here, $A = 231.67$, $r=0.059$, $n = 12$, and $t = 24$. First, calculate $(1+\frac{r}{n})^{nt}=(1+\frac{0.059}{12})^{12\times24}=(1 + 0.0049167)^{288}$. Using a calculator, $(1 + 0.0049167)^{288}\approx4.0077$. Then, $\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}=\frac{4.0077 - 1}{0.0049167}=\frac{3.0077}{0.0049167}\approx611.72$. $F=231.67\times611.72\approx141717.17$

Answer:

a) $2780$ b) $231.67$ c) $141717.17$