#382 Suppose a $100,000 T bondhas two years

Suppose a $100,000 T bondhas two years - Business Statistics

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Suppose a $100,000 T bondhas two years to maturity, a 5.68 % annual coupon rate for itssemiannual coupons, and a yield of 5.78%. Its price is $___. This price is quoted in points and 32nds as ___-____.

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Free Chegg Answer

Price$99,813.65          99    26/32

I use the finance calculator 2 P/YR   4N     5.78I/YR    100,000 FV

Given Data:

Amount of Interest in Period t (INT _t) = 5.68%

Required Rate of Return on Bond (k _d) = 5.78% (5.78/2= 2.89%)

Maturity Value in Period n (B _n) = $100,000

Number of years to Maturity = 2 years

Here Interest Payments are Semi-annualPayments:

           INT _t = $100,000*5.68% = $5680

           B₀ = ²ⁿΣ_t=1 { ½(INT _t) / (1+k_d/2)^t} + {B _n /(1+k_d/2)²ⁿ }

                 =^2*2Σ_t=1 {½ ($5680) /(1+0.0289)^t } + {$100,000 /(1+0.0289)^2*2=4

                 =⁴Σ_t=1 {$2840/1.0289} + {$100,000/(1.0289)⁴ }

           

                 = $10,584.39 +$89,229.27 (using Present Value Tables)

                 = $99,813.66

           B₀ = $99,813.66

The Price is quoted in points and 32ndsas: 99   26/32