Question

you want to retire with $2,169,000.00 in your mutual fund account. you will invest for 29 years. the mutual fund reports an average return of 11.07% over the 29 - 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? use this formula: $pmt=\frac{fv\times\frac{r}{n}}{(1 + \frac{r}{n})^{nt}-1}$ enter the dollar amount rounded to the nearest cent. your answer: answer

Explanation:

Step1: Identify the values

$FV = 2169000$, $r=0.1107$, $n = 4$ (quarter - compounding), $t = 29$.

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

The interest rate per period $i=\frac{r}{n}=\frac{0.1107}{4}=0.027675$. The number of periods $m=nt=4\times29 = 116$.

Step3: Substitute values into the formula

$pmt=\frac{FV\times i}{(1 + i)^{m}-1}=\frac{2169000\times0.027675}{(1 + 0.027675)^{116}-1}$.
First, calculate $(1 + 0.027675)^{116}$. Let $x=(1 + 0.027675)^{116}$. Using the formula $a^{b}=e^{b\ln(a)}$, we have $\ln(x)=116\times\ln(1.027675)\approx116\times0.0273 = 3.1668$. So $x = e^{3.1668}\approx23.777$.
Then, $pmt=\frac{2169000\times0.027675}{23.777 - 1}=\frac{60037.075}{22.777}\approx2636.73$.

Answer:

$2636.73$