question 1 (3 points)\nyou decide to invest $975.00 quarterly in a mutual fund that reports an average…

question 1 (3 points)\nyou decide to invest $975.00 quarterly in a mutual fund that reports an average return of 11.03% over the 30 - year life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will your mutual fund account be worth after 30 years?\nuse this formula:\n$fv = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer

question 1 (3 points)\nyou decide to invest $975.00 quarterly in a mutual fund that reports an average return of 11.03% over the 30 - year life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will your mutual fund account be worth after 30 years?\nuse this formula:\n$fv = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer

Answer

Explanation:

Step1: Identify the values

$pmt = 975$, $r=0.1103$, $n = 4$ (quarter - ly compounding), $t = 30$

Step2: Calculate the exponent and the interest rate per period

The interest rate per period $i=\frac{r}{n}=\frac{0.1103}{4}=0.027575$ The number of periods $nt=4\times30 = 120$

Step3: Calculate the future - value formula

$FV=pmt\times\frac{(1 + i)^{nt}-1}{i}$ $FV = 975\times\frac{(1 + 0.027575)^{120}-1}{0.027575}$ First, calculate $(1 + 0.027575)^{120}$. Let $x=(1 + 0.027575)^{120}$. Using the formula $a^b=e^{b\ln(a)}$, we have $\ln(x)=120\times\ln(1.027575)\approx120\times0.0272 = 3.264$. So $x = e^{3.264}\approx26.187$. Then, $\frac{(1 + 0.027575)^{120}-1}{0.027575}=\frac{26.187-1}{0.027575}=\frac{25.187}{0.027575}\approx913.40$. Finally, $FV=975\times913.40 = 890565$

Answer:

$890565.00$