Question

how much money should be deposited today in an account that earns 6.48% compounded semiannually so that it will accumulate to $18,300 in 13 years?
use this formula:
$pv = \frac{fv}{(1+\frac{r}{n})^{nt}}$
enter the dollar amount rounded up to the nearest cent.
your answer:

Explanation:

Step1: Identify given values

$FV = 18300$, $r = 0.0648$, $n = 2$, $t = 13$

Step2: Calculate periodic rate & total periods

$\frac{r}{n} = \frac{0.0648}{2} = 0.0324$, $nt = 2 \times 13 = 26$

Step3: Compute denominator

$(1 + 0.0324)^{26} \approx 2.3197$

Step4: Calculate present value

$PV = \frac{18300}{2.3197} \approx 7888.85$

Step5: Round up to nearest cent

Since the calculated value is already at the hundredths place, no further rounding up is needed.

Answer:

$\$7888.85$