how much would you have to deposit in an account with a 5% interest rate, compounded annually, to have $1300…

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.

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.

Answer

Explanation:

Step1: Identify the values given

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

Step2: Rearrange the compound - interest formula

The compound - interest formula is $F = P(1+\frac{r}{n})^{nt}$. We want to solve for $P$, so $P=\frac{F}{(1 +\frac{r}{n})^{nt}}$.

Step3: Substitute the values into the formula

$P=\frac{1300}{(1+\frac{0.05}{1})^{1\times13}}=\frac{1300}{(1 + 0.05)^{13}}$.

Step4: Calculate $(1 + 0.05)^{13}$

$(1 + 0.05)^{13}\approx1.885649$.

Step5: Calculate $P$

$P=\frac{1300}{1.885649}\approx689.43$.

Answer:

$689.43$