question 16 (4.5 points) you decide to invest $1,500.00 quarterly in a mutual fund that reports an average…

question 16 (4.5 points) you decide to invest $1,500.00 quarterly in a mutual fund that reports an average return of 11.19% over the 26 - 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 26 years? use this formula: $fv = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$. enter the dollar amount rounded to the nearest cent. your answer: answer

question 16 (4.5 points) you decide to invest $1,500.00 quarterly in a mutual fund that reports an average return of 11.19% over the 26 - 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 26 years? use this formula: $fv = pmt\times\frac{(1 + \frac{r}{n})^{nt}-1}{\frac{r}{n}}$. enter the dollar amount rounded to the nearest cent. your answer: answer

Answer

Explanation:

Step1: Identify the values

$pmt = 1500$, $r=0.1119$ (annual interest rate), $n = 4$ (quarter - ly compounding), $t = 26$ years.

Step2: Calculate the interest rate per period and number of periods

The interest rate per period $i=\frac{r}{n}=\frac{0.1119}{4}=0.027975$, and the number of periods $nt=4\times26 = 104$.

Step3: Substitute into the future - value of an ordinary annuity formula

$FV=pmt\times\frac{(1 + i)^{nt}-1}{i}=1500\times\frac{(1 + 0.027975)^{104}-1}{0.027975}$. First, calculate $(1 + 0.027975)^{104}$. Let $x=(1 + 0.027975)^{104}$. Using a calculator, $\ln(x)=104\times\ln(1.027975)\approx104\times0.02759\approx2.87$. Then $x = e^{2.87}\approx17.68$. $FV=1500\times\frac{17.68 - 1}{0.027975}=1500\times\frac{16.68}{0.027975}$. $FV=1500\times596.247$. $FV = 894370.5$.

Answer:

$894370.50$