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Issuing bonds at discount - computing effective interest rate
In this case the market interest rate is the discount rate that sets equal the market price (current value) of the bond to its present value. To find the market interest rate which is also referred to as promised yield YTM you would have solve for the interest rate in the bond price formula A market price of bond is the sum of discounted coupons and the terminal value of the bond. Most spreadsheet programs and calculators have a RATE function that makes possible finding this market interest rate. First see this for finding a coupon paying bond price The coupon payments are discounted so is the par value of the bond and sum of such discounts is the market price of the bond. The TVM functions in Excel and calculators make this possible using the following equation Let us take your data, 9% $100,000 coupon with 5 years remaining to maturity with market interest rate of 10%. Bonds issued in the US mostly pay two coupons per year. Thus we are finding the present value of 10 coupons each worth $4500 and par value of $100,000. The semi-annual market interest rate is 10%/2 or 5% The negative sign indicate money going out of hand Now solving for RATE is only possible using numerical methods and the RATE function is programmed using Newton-Raphson method to find one of the roots of the bond price equation. This rate will be the periodic rate in this case semi-annual rate which you have to multiply by 2 to get the annual rate. Do remember there is a difference between annual nominal rate and an annualized effective rate. To find the market interest rate  If you don't have Excel or a financial calculator then you may opt to use my version of these financial functions in this JavaScript library tadJS