$1.$ Your client is evaluating between the following two retirement options:

Option $1$: Pays a lump sum of P$2\mathrm{.}5$ million today.

Option $2$: A $10-$year annuity at P$180,000$ per year starting today,

If your client$$s required rate of return is $6$ percent per year

$$ i$.$ Which option will he prefer? $(7$ marks$)$

$$ ii$.$ At what interest rate will your client be indifferent between the two options?