Final answer:
To determine the purchase price of the bond, we calculated the total simple interest over 24 weeks and subtracted it from the final amount. The bond initially cost $988.14.
Step-by-step explanation:
To find out how much it cost to buy a corporate bond that pays $1,000 after 24 weeks at a simple interest rate of 0.05% per week, we first need to calculate the total interest earned over those 24 weeks. Then, we subtract that interest from the final payment to find the original price of the bond.
The total interest I is given by the formula I = P * r * t, where P is the principal amount (initial investment), r is the interest rate per period, and t is the number of periods.
First, we calculate the total interest earned:
- Total Interest (I) = Principal (P) * Interest Rate Per Week (r) * Number of Weeks (t)
- I = P * 0.0005 * 24
The given final amount is $1,000, which includes this interest. So, the principal can be calculated by subtracting the total interest from $1,000.
Principal (P) = Final Amount - Total Interest
- $1,000 = P + I
- $1,000 = P + (P * 0.0005 * 24)
- $1,000 = P * (1 + 0.0005 * 24)
- P = $1,000 / (1 + 0.0005 * 24)
Now we can plug in the numbers:
- P = $1,000 / (1 + 0.0005 * 24)
- P = $1,000 / (1 + 0.012)
- P = $1,000 / 1.012
- P = $988.14
Therefore, the bond cost $988.14 to buy.