PLEASE HELP IM INTELECTUALY NAIVE! On January 1, 2024, Universe of Fun issues $900,000, 8% bonds that mature in 10 years. The market interest rate for bonds of similar risk and maturity is 9%, and the bonds issue for $841,464. Interest is paid semiannually on June 30 and December 31.
Answers
PV = C x [(1 - (1 / (1 + r)^n)) / r] + FV / (1 + r)^n
where PV is the present value of the bond, C is the semiannual coupon payment, r is the semiannual market interest rate, n is the number of semiannual periods (which is 20 for a 10-year bond), and FV is the face value of the bond.
We know that the face value of the bond is $900,000, the semiannual coupon payment is 8% x $900,000 / 2 = $36,000, the market interest rate is 9% / 2 = 0.045, and the number of periods is 20.
Using these values, we can calculate the present value of the bond as follows:
PV = $36,000 x [(1 - (1 / (1 + 0.045)^20)) / 0.045] + $900,000 / (1 + 0.045)^20
PV = $36,000 x 13.5906 + $344,746.73
PV = $841,464
So the bond will issue for $841,464.
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