When is the best time to retire, i$.$e$.,$ when to start taking out social security?

$1.$Let$$s make the following assumptions:

$$The official retirement age is $65($x$)$ and at that time, you receive $$24,000($a$)$ per year and this number will increase by $3\%$ every year $($denote this rate as i$,$ the annual inflation rate$).$ You will continue to receive money every year until you pass, say age $85($b$)$

$$The government also says that if you start taking out your social security differently than age $65,$ the amount that you can get is $6\%$ less than a for each year earlier than x and $6\%$ more than a for each year later than x$.$

$$You use an annual discount rate of $10\%$ in calculating NPV

$2.$Build a excel sheet with formulas model to answer the following questions:

$$Should you retire at age $62,65$ or $68?$ Why?

$$Will your answer to the above question change if the life expectancy $($b$)$ is $90$ instead of $85?$ Why?

Your model should be just one sheet $($instead of multiple duplicate sheets$).$ Your model should work even when you change your decision $($x$)$ or any parameters of your model $($a$,$ i$,$ b$)$