Question $3($in$-$slide calculation of duration and duration gap$)$

Solve the following numerical question on duration and duration gap. Show how you arrive at your answers.

Bank ABC has the following $2$ bond$-$like loans:

Loan $1$: $$1$m principal, $3$ years maturity, annual interest payment fixed at $10\%$

Loan $2$: $$1$m principal, $5$ years maturity, annual interest payment fixed at $12\%$

The market interest rate is now at $5\%.$ What is the duration of the bank$$s loan portfolio? If the market interest rate increases by $1\%$ now, what will be the percentage change of the present value of the portfolio?

Furthermore, it has $$1\mathrm{.}5$m of liabilities $($at market value$)$ with a duration of $2\mathrm{.}68$ years. How much will the value of the bank change due to the change in interest rate?