Original practice · fully worked
Original variant: one-year bond allocation required to close a later shortfall
A reserve must pay 1,000 at year 1 and 1,100 at year 2. A two-year zero-coupon holding will provide 950 at year 2. Money remaining after the first payment can earn 6% for year 2. How much must be invested today in a one-year zero-coupon bond yielding 5%?
- A
924.08 - B
978.44 - C
1,032.79 - D
1,087.15 - E
1,141.51
Answer and calculation
The year-2 bond leaves a shortfall of 150, requiring 141.51 at year 1. The one-year bond must therefore mature to 1,141.51, so its initial cost is 1,087.15, choice D.
Setup
Setup
Work backward from year 2 to find the surplus that must remain immediately after the year-1 payment.
S1(1.06)=1100−950 Model
Model
The one-year bond must mature to the first liability plus that required surplus.
1.05X=1000+S1 Compute
Compute
The required year-1 surplus is 141.51, giving an initial one-year bond investment of 1087.15.
X=1.051000+150/1.06=1087.151842 Answer
Answer
The required investment is 1087.15, which is choice D.
X≈1087.15(D) 