Final answer:
The original cost of the corporate bond is calculated using the simple interest formula, with a principal purchase price of approximately $1,992.88 after rounding to the nearest cent.
Step-by-step explanation:
To calculate the original cost of the corporate bond with a simple interest rate, we must first determine the total amount of interest earned.
Using the formula I = Prt, where I is the interest, P is the principal (initial amount), r is the rate, and t is the time (in weeks), we can calculate the principal.
The bond pays out $2,000 and earns a simple interest of 0.03% per week for 12 weeks.
First, we convert the interest rate to decimal by dividing by 100: 0.03% / 100 = 0.0003.
Then, multiply the interest rate by the number of weeks: 0.0003 * 12 = 0.0036.
To find the principal, we rearrange the formula to P = I / (rt). The interest earned (I) can be calculated as the final amount minus the principal.
If we let P be the principal and $2,000 be the final amount (A), then P + I = A, so I = A - P. We substitute into the rearranged formula to get P = (A - P) / (rt).
Solving for P, we get P(A - P) = I.
Substituting values, we have P(0.0036) = $2,000 - P.
Solving for P, we get P = $2,000 / (1 + 0.0036).
After the calculation, the original cost of the bond is approximately $1,992.88 when rounded to the nearest cent.