Final answer:
To achieve a 5% effective annual return over four years on a bond bought for $180,000 and sold after collecting annual interest, it needs to be sold for $178,791.13, which accounts for both the $40,000 interest earned and the growth in the initial investment due to compound interest.
Step-by-step explanation:
To calculate the sale price for the bond that would yield a 5% effective annual return on the investment after four years, we need to take into account the initial investment of $180,000 and the annual interest of 5% on the bond's face value of $200,000. The interest received each year would be $200,000 * 5% = $10,000. Over four years, the total interest earned is $10,000 * 4 = $40,000. To achieve a 5% yield, the total return over four years, which includes both the interest earned and the capital gains from the sale, must be equal to the initial investment plus 5% each year, compounded annually. This total future value (FV) can be calculated using the formula FV = PV * (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years. In this case, FV = $180,000 * (1 + 0.05)^4.
After calculating the future value, you subtract the interest earned to find the necessary sale price of the bond after four years to provide a 5% return. The calculation would be as follows: Future Value = $180,000 * (1 + 0.05)^4 = $180,000 * 1.21550625 = $218,791.13. Therefore, the sale price needed for the bond to yield a 5% return over four years would be $218,791.13 - $40,000 in interest = $178,791.13.