12 formula 5 points how much would you need to deposit in an account now in order to have $1,000 in the…

12 formula 5 points how much would you need to deposit in an account now in order to have $1,000 in the account in 24 years? assume the account earns 3.1% interest compounded semiannually. round to the cent answer

12 formula 5 points how much would you need to deposit in an account now in order to have $1,000 in the account in 24 years? assume the account earns 3.1% interest compounded semiannually. round to the cent answer

Answer

Explanation:

Step1: Identify compound - interest formula

The compound - interest formula for present value is $P = \frac{A}{(1+\frac{r}{n})^{nt}}$, where $A$ is the future value, $P$ is the present value, $r$ is the annual interest rate (in decimal form), $n$ is the number of times interest is compounded per year, and $t$ is the number of years.

Step2: Convert given values to appropriate form

We have $A = 1000$, $r=0.031$ (since $3.1%=0.031$), $n = 2$ (compounded semiannually), and $t = 24$.

Step3: Substitute values into the formula

$P=\frac{1000}{(1 +\frac{0.031}{2})^{2\times24}}$. First, calculate the value inside the parentheses: $\frac{0.031}{2}=0.0155$, and $1+\frac{0.031}{2}=1.0155$. Then, calculate the exponent: $2\times24 = 48$. So, $(1.0155)^{48}\approx2.1977$. Then, $P=\frac{1000}{2.1977}\approx454.93$.

Answer:

$454.93$