how much would you have to deposit in an account with a 8% interest rate, compounded monthly, to have $800…

how much would you have to deposit in an account with a 8% interest rate, compounded monthly, to have $800 in your account 8 years later?\n$p = \\$?$\n$f = p(1 + \\frac{r}{n})^{nt}$\nround to the nearest cent.

how much would you have to deposit in an account with a 8% interest rate, compounded monthly, to have $800 in your account 8 years later?\n$p = \\$?$\n$f = p(1 + \\frac{r}{n})^{nt}$\nround to the nearest cent.

Answer

Explanation:

Step1: Define given variables

$F = 800$, $r = 0.08$, $n = 12$, $t = 8$

Step2: Rearrange formula for P

$P = \frac{F}{(1 + \frac{r}{n})^{nt}}$

Step3: Substitute values into formula

$P = \frac{800}{(1 + \frac{0.08}{12})^{12 \times 8}}$

Step4: Calculate denominator terms

First, $\frac{0.08}{12} \approx 0.006667$, $12 \times 8 = 96$ Then, $(1 + 0.006667)^{96} \approx 1.9058$

Step5: Compute final P value

$P \approx \frac{800}{1.9058} \approx 419.77$

Answer:

$$419.77$