determine the present value p that must be invested to have the future value a at simple interest rate r…

determine the present value p that must be invested to have the future value a at simple interest rate r after time t. a = $7000.00, r = 11.5%, t = 6 months $ (do not round until the final answer. then round up to the nearest cent as needed.)

determine the present value p that must be invested to have the future value a at simple interest rate r after time t. a = $7000.00, r = 11.5%, t = 6 months $ (do not round until the final answer. then round up to the nearest cent as needed.)

Answer

Explanation:

Step1: Convert time to years

Since $t = 6$ months, and 1 year has 12 months, $t=\frac{6}{12}=0.5$ years.

Step2: Use simple - interest formula for present value

The formula for simple interest is $A = P(1+rt)$. We can solve for $P$: $P=\frac{A}{1 + rt}$. Substitute $A = 7000$, $r=0.115$ (since $11.5%=0.115$), and $t = 0.5$ into the formula. $P=\frac{7000}{1+0.115\times0.5}$

Step3: Calculate the value of $P$

First, calculate the denominator: $1+0.115\times0.5=1 + 0.0575=1.0575$. Then, $P=\frac{7000}{1.0575}\approx6628.84$.

Answer:

$6628.84$