you decide to invest $1,025.00 quarterly in a mutual fund that reports an average return of 9.98% over the…

you decide to invest $1,025.00 quarterly in a mutual fund that reports an average return of 9.98% over the 25 - 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 25 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

you decide to invest $1,025.00 quarterly in a mutual fund that reports an average return of 9.98% over the 25 - 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 25 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

$pmt = 1025$, $r=0.0998$, $n = 4$ (quarter - compounding), $t = 25$.

Step2: Calculate the exponent

$nt=4\times25 = 100$.

Step3: Calculate the value inside the parentheses

$1+\frac{r}{n}=1+\frac{0.0998}{4}=1 + 0.02495=1.02495$.

Step4: Calculate the numerator of the fraction

$(1+\frac{r}{n})^{nt}-1=(1.02495)^{100}-1$. Using a calculator, $(1.02495)^{100}\approx11.02777$, so $(1.02495)^{100}-1\approx10.02777$.

Step5: Calculate the denominator of the fraction

$\frac{r}{n}=\frac{0.0998}{4}=0.02495$.

Step6: Calculate the fraction value

$\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}=\frac{10.02777}{0.02495}\approx401.9146$.

Step7: Calculate the future - value

$FV=pmt\times\frac{(1+\frac{r}{n})^{nt}-1}{\frac{r}{n}}=1025\times401.9146\approx411962.47$.

Answer:

$411962.47$