A company plans to invest X at the beginning of each month in a zero-coupon bond in order to accumulate 100,000 at the end of six months. The price of each bond as a percentage of redemption value is given in the following chart:
| Maturity (months) | 1 | 2 | 3 | 4 | 5 | 6 |
| Price | 99% | 98% | 97% | 96% | 95% | 94% |
Calculate X given that the bond prices will not change during the six-month period.
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
Solution: B
The accumulated value is the reciprocal of the price. The equation is X[(1/0.94)+(1/0.95)+(1/0.96)+(1/0.97)+(1/0.98)+(1/0.99)] = 100,000. X= 16,078
Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.