Original practice · fully worked
Original variant: coupon rate from a discounted heritage bond
A five-year heritage bond has face 1,000, redemption 950, annual coupons at rate r on face, and annual effective yield 4%. Its price is 920. Determine r.
- A
2.50% - B
2.80% - C
3.13% - D
3.50% - E
4.00%
Answer and calculation
Removing the discounted redemption from price and dividing by the coupon annuity factor gives r = 3.13%, choice C.
Setup
Setup
Separate the unknown coupon annuity from the known discounted redemption.
920=1000ra5∣0.04+950(1.04)−5 Model
Model
The residual price after removing redemption is the present value of five level coupons of 1,000r.
1000ra5∣=920−950(1.04)−5 Compute
Compute
Dividing by the five-year annuity factor and face amount gives rate 0.0312612.
r=0.0312612 Answer
Answer
The annual coupon rate is approximately 3.13%, choice C.
r=3.13%(C) Calculator reproduction
BA II Plus keystrokes
- 2nd CLR TVM; 2nd I/Y; 1 ENTER; ↓; 1 ENTER; 2nd CPT; 2nd PMT; if BGN is displayed, 2nd ENTER; 2nd CPT; 5 N; 4 I/Y; 920 +/- PV; 0 PMT; 950 FV; CPT PMTPMT = 31.2612END mode; I/Y is annual. Divide the positive coupon by face 1,000 for the coupon rate.
