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Issuing bonds at discount - computing effective interest rate
If the market rate and coupon were equal, the bond would be valued at face value, by definition. (Not 100% true, but this is an exercise, and that would be tangent to this discussion).  Since the market rate is higher than the coupon rate, the value I am willing to pay drops a bit, so my return is the same as the market rate.  This can be done by hand, a time value of money calculation for each payment. Discount by the years till received at the market rate to get the present value for each payment, and sum up the numbers.  The other way is to use a finance calculator and solve for rate.  The final payment of $10,000 (ignore final coupon just now) is $10,000/(1.1^5). In other words, that single chunk of cash is worth 10% less if it's one year away, (1.1)^2 if 2 years away, etc.  Draw a timetable with each payment and divide by 1.1 for each year it's away from present. If the 9% coupon is really 4.5% twice a year, it's $450 in 6 month intervals, and each 6 mo interval is really 5% you discount.  Short durations like this can be done by hand, a 30 year bond with twice a year payments is a pain.  Welcome to Money.SE.