Question

step 2
ultimately, we will use the equation $i = fv - pv$, but first we must calculate $fv$ and identify $pv$.
recall the future value of compound interest formula $fv = pv\left(1 + \frac{r}{n}\
ight)^{nt}$ where $pv$ is the present value, $r$ is the annual interest
rate, $n$ is the number of compounding periods per year, and $t$ is the number of years.
an investment of $8,200 is deposited into an account paying 8% interest compounded semiannually or twice a year, for 6
years.
determine the present value $pv$. this value is in dollars, but we leave off the unit for the formula.
$pv = \square$
the interest rate is given as a percent, but the formula requires a decimal. to rewrite a percent as a decimal, move the decimal
point two places to the left and remove the percent sign.
determine the interest rate $r$ (as a decimal).
$r = \square$
determine the compounding periods per year $n$.
$n = \square$
determine the time period $t$. this value is in years, but we leave off the unit for the formula.
$t = \square$

Explanation:

Step1: Identify present value PV

The initial investment is the present value, so $PV = 8200$.

Step2: Convert % to decimal for r

Divide 8 by 100: $r = \frac{8}{100} = 0.08$

Step3: Find compounding periods n

Semiannual means 2 periods/year: $n = 2$

Step4: Identify time period t

The investment lasts 6 years: $t = 6$

Answer:

$PV = 8200$
$r = 0.08$
$n = 2$
$t = 6$