Question 1
A 10-year bond has a face amount of $1,000 and pays semiannual coupons at an annual coupon rate of 8.0%. It is bought to yield a nominal annual rate of 6.0% convertible semiannually.
Calculate the price of the bond.
Bond price calculator, with steps
Find a bond's price from its yield, or its yield from its price. You get the working, the book value after every coupon and the BA II Plus keys.
Price
$1,148.77
A premium of $148.77
The working
- Coupons are paid twice a year, so work in half-years: coupons of , yield per half-year.
- Price
, with and . . - The price is above the redemption amount by : a premium, because each coupon is more than the yield requires.
On a BA II Plus
- Clear the five keys2ndCLR TVM
- One payment a period2ndP/Y1ENTER2ndQUIT
- Number of coupons20N
- Yield per period (%)3I/Y
- Coupon40PMT
- Redemption amount1000FV
- ComputeCPTPV
The price shows as a negative number: it is money you pay.
Book value, coupon by coupon
| Coupon | Amount | Interest earned | Premium written down | Book value |
|---|---|---|---|---|
| 1 | 40.00 | 34.46 | 5.54 | 1,143.24 |
| 2 | 40.00 | 34.30 | 5.70 | 1,137.54 |
| 3 | 40.00 | 34.13 | 5.87 | 1,131.66 |
| 4 | 40.00 | 33.95 | 6.05 | 1,125.61 |
| 5 | 40.00 | 33.77 | 6.23 | 1,119.38 |
| 6 | 40.00 | 33.58 | 6.42 | 1,112.96 |
| 7 | 40.00 | 33.39 | 6.61 | 1,106.35 |
| 8 | 40.00 | 33.19 | 6.81 | 1,099.54 |
| 9 | 40.00 | 32.99 | 7.01 | 1,092.53 |
| 10 | 40.00 | 32.78 | 7.22 | 1,085.30 |
Premium, par or discount?
| Coupon rate above the yield | Premium: the price is above the redemption amount |
|---|---|
| Coupon rate equal to the yield | Par: the price equals the redemption amount |
| Coupon rate below the yield | Discount: the price is below the redemption amount |
Semiannual coupons
Most exam bonds pay coupons twice a year, and both rates are quoted per year. Work in half-years: halve the coupon rate, halve the yield and double the number of years.
A 10-year bond with 8% coupons and a 6% yield is 20 coupons of 4% of face, discounted at 3% each.
Try it on an exam question
Question 2
A 10-year bond has a face amount of $1,000 and pays semiannual coupons at an annual coupon rate of 6.0% and is redeemable at par. It is bought for $925.00.
Calculate the yield, as a nominal annual rate convertible semiannually.
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Questions people ask
How do you calculate the price of a bond?
Add the present value of the coupons to the present value of the redemption amount, both at the yield per coupon period: price = coupon × a(n) + redemption × vⁿ. With semiannual coupons, halve the annual rates and double the number of years.
When does a bond sell at a premium?
When its coupon rate is higher than the yield. Each coupon is larger than the yield requires, so the buyer pays more than the redemption amount. When the coupon rate is lower than the yield, the bond sells at a discount.
How do you find a bond's yield on a BA II Plus?
Enter the number of coupons as N, the price as a negative PV, the coupon as PMT and the redemption amount as FV, then press CPT and I/Y. With semiannual coupons the result is the yield per half-year, so double it.
What is the book value of a bond?
The price of the remaining payments at the yield the bond was bought at. It moves from the purchase price to the redemption amount as coupons are paid.
What is amortization of premium?
The part of each coupon that is not interest earned. Interest earned is the yield times the book value; the rest of the coupon writes the book value down toward the redemption amount.