a newscaster earns $32,300 and wants to invest 10% of his/her salary to save for retirement in 33 years. if…

Answer:

a) $3230 b) $269.17 c) $311444.97

Explanation:

Step1: Calculate annual savings

Annual salary is $32300, 10% of it is $32300\times0.1 = 3230$.

Step2: Calculate monthly deposit

Annual savings is $3230, so monthly deposit is $\frac{3230}{12}\approx269.17$.

Step3: Identify compound - interest formula variables

The compound - interest formula for 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 deposit, $r$ 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, $A = 269.17$, $r=0.054$, $n = 12$, $t = 33$.

Step4: Calculate the exponent part

$(1+\frac{0.054}{12})^{12\times33}=(1 + 0.0045)^{396}\approx4.8799$.

Step5: Calculate the fraction part

$\frac{(1 + 0.0045)^{396}-1}{0.0045}=\frac{4.8799 - 1}{0.0045}=\frac{3.8799}{0.0045}\approx862.2$.

Step6: Calculate the future value

$F=269.17\times862.2\approx311444.97$.