Question #194827

A rs 5000 par value bond bearing a coupon rate of 10% will mature after 10 years. What is the price to buy the bond at today , if discounted rate is 12%

Expert's answer

**Bond Price = ∑(C**_{n }**/ (1+YTM)**^{n}** )+ P / (1+i)**^{n}

Where

**n =**Period which takes values from 0 to the nth period till the cash flows ending period**C**_{n }**=**Coupon payment in the nth period**YTM or i=**interest rate or required yield**P =**Par Value of the bond

"n=10years"

Cn=10% of 5000 = 500

YTM or i = 12%= 0.12

P= 5000

"1+Interest = 1+\\frac{12}{100}= 1.12"

"Bond Price =\\frac{500}{(1.12)}\n+\\frac{500}{(1.12)^{2}}+\\frac{500}{(1.12)^{3}}+ \\frac{500}{(1.12)^{4}}+ + \\frac{500}{(1.12)^{5}}\n+ \\frac{500}{(1.12)^{6}} + \\frac{500}{(1.12)^{7}}\n+ \\frac{500}{(1.12)^{8}}+ + \\frac{500}{(1.12)^{9}}+\n\\frac{500}{(1.12)^{10}}+\\frac{5000}{(1.12)^{10}}"

"BondPrice = 446.43+398.60+ 345.90+317.76+283.71+253.32+226.17+201.94+170.31+160.99 + 1609.87=4415"

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