a$)$ Based on the table below, calculate the duration gap for the bank.

$($b$)$ Estimate the change in equity in absolute and percentage terms if interest rates move from their current level of $4\%$ up to $5\mathrm{.}25\%.$

$$

Instrument

Value

Duration

$$

$$

$$

Cash

$70$

$0$

ARM Mortgages

$300$

$0\mathrm{.}15$

Fixed Rate Mortgages

$200$

$20$

Investments in Securities

$100$

$10$

$$

$$

$$

Total Assets

$570$

$$

$$

$$

$$

$$

$$

$$

Deposits

$400$

$0$

Loans from other Banks

$100$

$6$

Equity

$70$

$?$