Currently, people retiring at age $67$ are entitled to "full" retirement benefits; those retiring at age $62$ are eligible for only $70\%$ of "full" benefits. Suppose a person is contemplating retirement at age $62.$ If the person retires at $67,$ they will receive $$1,359$ per month. $($Ignore time value of money considerations for this problem.$)$

REQUIRED

a$.$ How large is the reduction in monthly benefits if a person retires at age $62?$

$$Note: Enter the answer in dollars and cents, rounded to the nearest penny.

$Answer $1$

$407\mathrm{.}7$

b$.$ What is the break$-$even age at which the benefits from delaying retirement until age $67$ equal the cumulative benefits from retiring at age $62?$

Note: Round your answer to the nearest month, enter $7$ for $7\mathrm{.}4$ months, or $8$ for $7\mathrm{.}5$ months.

Answer $2$

years Answer $3$

$0$

months