Question

you decide to invest $1,450.00 quarterly in a mutual fund that reports an average return of 9.64% 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
view hint for question 6
question 7 (10 points)
you decide to invest $875.00 quarterly in a mutual fund that reports an average return of 10.92% over the 29-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 29 years?
use this formula:

Explanation:

Step1: Define variables for Q6

$pmt = 1450$, $r = 0.0964$, $n = 4$, $t = 25$

Step2: Calculate total periods for Q6

$nt = 4 \times 25 = 100$

Step3: Calculate periodic rate for Q6

$\frac{r}{n} = \frac{0.0964}{4} = 0.0241$

Step4: Compute future value for Q6

$FV = 1450 \times \frac{(1+0.0241)^{100} - 1}{0.0241}$
First, $(1+0.0241)^{100} \approx 10.9381$
Then, $\frac{10.9381 - 1}{0.0241} = \frac{9.9381}{0.0241} \approx 412.3693$
Finally, $1450 \times 412.3693 \approx 597935.49$

Step5: Define variables for Q7

$pmt = 875$, $r = 0.1092$, $n = 4$, $t = 29$

Step6: Calculate total periods for Q7

$nt = 4 \times 29 = 116$

Step7: Calculate periodic rate for Q7

$\frac{r}{n} = \frac{0.1092}{4} = 0.0273$

Step8: Compute future value for Q7

$FV = 875 \times \frac{(1+0.0273)^{116} - 1}{0.0273}$
First, $(1+0.0273)^{116} \approx 23.1972$
Then, $\frac{23.1972 - 1}{0.0273} = \frac{22.1972}{0.0273} \approx 813.0842$
Finally, $875 \times 813.0842 \approx 711448.68$

Answer:

Question 6: $\$597,935.49$
Question 7: $\$711,448.68$