you want to retire with $2,581,000.00 in your mutual fund account. you will invest for 28 years. the mutual…

you want to retire with $2,581,000.00 in your mutual fund account. you will invest for 28 years. the mutual fund reports an average return of 12.11% over the 28 - year - long life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will you need to pay quarterly into your mutual fund to reach your goal?\nuse this formula:\n$pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer\nquestion 18 (4.5 points)\nyou decide to invest $950.00 quarterly in a mutual fund that reports an average return of 9.34% over the 15 - year life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will your mutual fund account be worth after 15 years?\nuse this formula:\n$fv = pmt\times\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:

you want to retire with $2,581,000.00 in your mutual fund account. you will invest for 28 years. the mutual fund reports an average return of 12.11% over the 28 - year - long life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will you need to pay quarterly into your mutual fund to reach your goal?\nuse this formula:\n$pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$\nenter the dollar amount rounded to the nearest cent.\nyour answer:\nanswer\nquestion 18 (4.5 points)\nyou decide to invest $950.00 quarterly in a mutual fund that reports an average return of 9.34% over the 15 - year life of the mutual fund. assuming that this interest rate continues, and is compounded quarterly, how much will your mutual fund account be worth after 15 years?\nuse this formula:\n$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 values for first problem

$FV = 2581000$, $r=0.1211$, $n = 4$, $t = 28$.

Step2: Calculate the quarterly interest rate and number of periods

$i=\frac{r}{n}=\frac{0.1211}{4}=0.030275$, $nt=4\times28 = 112$.

Step3: Substitute values into the formula

$pmt=\frac{FV\times i}{(1 + i)^{nt}-1}=\frac{2581000\times0.030275}{(1 + 0.030275)^{112}-1}$. First, calculate $(1 + 0.030275)^{112}\approx24.9797$. Then, $(1 + 0.030275)^{112}-1\approx23.9797$. And $2581000\times0.030275 = 78130.775$. So $pmt=\frac{78130.775}{23.9797}\approx3258.11$.

Step4: Identify values for second problem

$pmt = 950$, $r = 0.0934$, $n=4$, $t = 15$.

Step5: Calculate the quarterly interest rate and number of periods

$i=\frac{r}{n}=\frac{0.0934}{4}=0.02335$, $nt=4\times15=60$.

Step6: Substitute values into the formula

$FV=pmt\times\frac{(1 + i)^{nt}-1}{i}=950\times\frac{(1 + 0.02335)^{60}-1}{0.02335}$. First, calculate $(1 + 0.02335)^{60}\approx4.1777$. Then, $(1 + 0.02335)^{60}-1\approx3.1777$. And $\frac{(1 + 0.02335)^{60}-1}{0.02335}=\frac{3.1777}{0.02335}\approx136.082$. So $FV=950\times136.082=129277.90$.

Answer:

$3258.11$ $129277.90$