question 6 (10 points)\nyou decide to invest $500.00 quarterly in a mutual fund that reports an average…

question 6 (10 points)\nyou decide to invest $500.00 quarterly in a mutual fund that reports an average return of 9.52% over the 28 - year life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will your mutual fund accou be worth after 28 years?\nuse this formula:\n$fv = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:

question 6 (10 points)\nyou decide to invest $500.00 quarterly in a mutual fund that reports an average return of 9.52% over the 28 - year life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will your mutual fund accou be worth after 28 years?\nuse this formula:\n$fv = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:

Answer

Explanation:

Step1: Identify the values

$pmt = 500$, $r=0.0952$, $n = 4$ (quarter - ly compounding), $t = 28$.

Step2: Calculate the exponent

$nt=4\times28 = 112$.

Step3: Calculate the value inside the parentheses

$1+\frac{r}{n}=1+\frac{0.0952}{4}=1 + 0.0238=1.0238$.

Step4: Calculate $(1+\frac{r}{n})^{nt}$

$(1.0238)^{112}\approx13.1347$.

Step5: Calculate $(1+\frac{r}{n})^{nt}-1$

$13.1347 - 1=12.1347$.

Step6: Calculate $\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}$

$\frac{12.1347}{0.0238}\approx510.6933$.

Step7: Calculate the future - value

$FV=pmt\times\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}=500\times510.6933 = 255346.65$.

Answer:

$255346.65$