Question

how much would you have to deposit in an account with a 5% interest rate, compounded annually, to have $1300 in your account 13 years later? p = $? f = p(1 + \frac{r}{n})^{nt} round to the nearest cent.

Explanation:

Step1: Identify given values

$F = 1300$, $r = 0.05$, $n = 1$, $t = 13$

Step2: Rearrange formula for $P$

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

Step3: Substitute values into formula

$P = \frac{1300}{(1 + \frac{0.05}{1})^{1 \times 13}}$

Step4: Simplify denominator

$(1 + 0.05)^{13} = 1.05^{13} \approx 1.885649$

Step5: Calculate $P$

$P = \frac{1300}{1.885649} \approx 689.42$

Answer:

$\$689.42$