Using a discount rate of $1\%$ compounded annually, a pension fund estimates that the present

value of its assets and liabilities are $$9$ million and $$6$ million, respectively. The duration of the

assets is $13$ years and the duration of the liabilities is $23$ years.

$($a$)$ Suppose that the interest rate decreases to $0\mathrm{.}93\%.$ Estimate the relative changes in the fund's

assets and liabilities. Express yours answers as percentages, to the nearest basis point.

Relative Change in Assets ~~

Relative Change in Liabilities ~~

$($b$)$ Using your rounded answers from $($a$),$ estimate the absolute changes in the fund's assets and

liabilities. Express your answers in millions of dollars, to the nearest thousand.

Absolute Change in Assets ~~$

million

Absolute Change in Liabilities ~~$

million

$($c$)$ The fund's net worth is defined as the difference between its assets and liabilities. Using your

answers from $($b$),$ estimate the relative change in the fund's net worth. Express your answer as a

percent, to the nearest basis point.

Relative Change ~~