Independent solution

How to solve this Liability Matching with Mortgages question

Setup

Setup

Let X and Y be the amounts invested in the two mortgages. Determine Y from the mortgage whose two level receipts supply the recurring 1,000 liability.

Y/a2‾∣ 0.07=1000⟹Y=1808.02Y/a_{\overline2|\,0.07}=1000\Longrightarrow Y=1808.02

Model

Model

The two-year annuity equation gives Y = 1,808.02. At the first liability date, the other mortgage’s accumulated value plus the 1,000 receipt must equal 2,000.

1.06X+1000=2000⟹X=943.401.06X+1000=2000\Longrightarrow X=943.40

Compute

Compute

That equation gives X = 943.40. Total initial investment is 943.40 + 1,808.02 = 2,751.42, or 2,751.

X+Y=2751.42X+Y=2751.42

Answer

Answer

The calculation gives 2751 for liability matching with mortgages, matching published choice C.

X+Y=2751(C)\boxed{X+Y=2751\quad\text{(C)}}