Have you seen $20,000?
You own a bond that will pay 7% per year for the next 10 years, on a principal of $20,000. If the prevailing discount rate is 10% throughout, what is the bond worth now?
The answer is 16313.26.
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3 solutions
The price of a bond is determined by the present value of the coupon payments. Hence, it is equal to
( 1 . 1 ) 1 0 2 0 0 0 0 + i = 1 ∑ 1 0 ( 1 . 1 ) i 1 4 0 0 .
This gives us the value of 16313.26
Note that since the interest rate is lower than the discount rate, hence this bond trades at a discount.
Ok so there's a summation associated with it . Actually sir, a friend(who has taken commerce) has helped me out, no it was he who gave me the answer .
But your solution is clearer .
The present value of a coupon bond can be calculated as: PV= CPN * y 1 * (1- ( 1 + y ) N 1 ) + ( 1 + y ) N F V
- CPN is the Coupon the bond pays.
- y is the discount rate, also known as the Yield to Maturity.
- N is the number of periods.
- FV is the Future value.
Inserting the variables gives: PV= (0.07*20,000) * 0 . 1 1 * (1- ( 1 + 0 . 1 ) 1 0 1 ) + ( 1 + 0 . 1 ) 1 0 2 0 , 0 0 0 = 16313.26
I solved it using a spreadsheet: