Final answer:
To have $3,000 in 8 months with an annual simple interest rate of 7%, you would need to deposit approximately $2,864.32 today.
Step-by-step explanation:
To calculate how much you need to invest today to have $3,000 in 8 months with an annual simple interest rate of 7%, you can use the formula for simple interest: I = PRT, where I is the interest earned, P is the principal amount (the initial amount of money), R is the annual interest rate (as a decimal), and T is the time the money is invested (in years).
First, convert the interest rate from a percentage to a decimal by dividing by 100: 7% = 0.07. Next, convert the time period from months to years. Since there are 12 months in a year, 8 months is ⅓ year or approximately 0.667 years.
Now, set up the equation with the known values and solve for P:
$I = PRT$
$3000 = P × 0.07 × 0.667$
We're actually looking for the total amount A, which includes both the principal P and the interest I. The final amount A is $3,000, so:
A = P + I or in our case P + PRT = A. Since I is part of A, we need to subtract the interest earned over 8 months from the final amount to find P.
Rearranging the formula and solving for P gives us:
P = A / (1 + RT)P = $3,000 / (1 + 0.07 × 0.667)P approximately equals $2,864.32.
Therefore, you would need to deposit approximately $2,864.32 today to have it grow to $3,000 in 8 months at an annual simple interest rate of 7%.