a person deposits $1000 into a mutual fund containing stocks at the end of each semiannual period for 16…

a person deposits $1000 into a mutual fund containing stocks at the end of each semiannual period for 16 years. assume the fund earns 6% compounded semiannually and find the future value. click the icon to view the amount of an annuity table. the future value is approximately $ (round to the nearest cent as needed.)

a person deposits $1000 into a mutual fund containing stocks at the end of each semiannual period for 16 years. assume the fund earns 6% compounded semiannually and find the future value. click the icon to view the amount of an annuity table. the future value is approximately $ (round to the nearest cent as needed.)

Answer

Explanation:

Step1: Identify the variables

$P = 1000$, $r=0.06$, $n = 2$ (semi - annual compounding), $t = 16$ The number of periods $m=nt=2\times16 = 32$ The interest rate per period $i=\frac{r}{n}=\frac{0.06}{2}=0.03$

Step2: Use the future - value of an ordinary annuity formula

The formula for the future value of an ordinary annuity is $F = P\times\frac{(1 + i)^{m}-1}{i}$ Substitute $P = 1000$, $i = 0.03$, and $m = 32$ into the formula: $F=1000\times\frac{(1 + 0.03)^{32}-1}{0.03}$ First, calculate $(1 + 0.03)^{32}$: $(1 + 0.03)^{32}\approx2.575084$ Then, $(1 + 0.03)^{32}-1\approx2.575084 - 1=1.575084$ $\frac{(1 + 0.03)^{32}-1}{0.03}=\frac{1.575084}{0.03}\approx52.5028$ $F = 1000\times52.5028=52502.78$

Answer:

$52502.78$