Final answer:
To find the cost of the corporate bond initially, the formula for simple interest is used, resulting in an approximate purchase price of $3,960.31.
Step-by-step explanation:
The question involves calculating the initial cost of a corporate bond that pays out $4,000 after 18 weeks and earns 0.06% simple interest per week. To find the purchase price of the bond, we employ the formula for simple interest: I = P * r * t, where I is the interest, P is the principal amount (initial investment), r is the interest rate per period, and t is the number of time periods.
Given that the interest earned on the bond over 18 weeks is I = $4,000 - P (since the $4,000 includes the original investment plus the interest), the interest rate per week is r = 0.0006, and the number of weeks is t = 18, we can rearrange the formula to solve for P: P = I / (r * t). Substituting the known values, we can calculate the initial investment P.
Therefore, the cost to buy the bond initially would be calculated as follows:
P(0.0108 + 1) = $4,000
P ≈ $3,960.31
The bond, therefore, cost approximately $3,960.31 to buy initially, rounded to the nearest cent.