You have just turned $60$ and have decided to retire. You have sufficient retirement savings to get by without taking Canada Pension Plan $($CPP$)$ benefits, but you wish to decide between your different CPP options. You qualify for the maximum benefit of $$1364\mathrm{.}60$ per month if you start taking CPP at age $65.$

If you start taking CPP benefits before age $65,$ your pension is reduced by $0\mathrm{.}6\%$ of the monthly payment for every month before age $65$ that you receive pension payments. For example, if you take decide to start taking benefits $2$ months before age $65,$ your monthly benefit is reduced by $2x0\mathrm{.}6\%=1\mathrm{.}2\%.$ So instead of receiving $$1364\mathrm{.}60$ per month, you receive $$1364\mathrm{.}60-1\mathrm{.}2\%x1364\mathrm{.}60=$$$1348\mathrm{.}22$ per month, starting at age $64$ and $10$ months.

If you delay taking your CPP benefits until after age $65,$ your monthly income will increase by $0\mathrm{.}7\%$ for each month that you delay, up until age $70.$ For example, if you decide to start taking benefits $2$ months after age $65,$ your monthly benefit is increased by $20\mathrm{.}7\%=1\mathrm{.}4\%.$ So you will now receive $$1364\mathrm{.}60+1\mathrm{.}4\%$ x $1364\mathrm{.}60=$$$1383\mathrm{.}70.$

The current life expectancy for someone of your age and other characteristics is $85.$ You decide to plan as if you will die at age $85.$

Assume the discount rate is $0\mathrm{.}4\%$ per month.

Assume that the first payment will always occur in one month, so that the formula$/$calculator will always give you PV at time $0,$ and you will not have to add additional payments, i$.$e$.5$ years $=60$ payments.

a$)$ What is the amount of your monthly CPP payment if you take benefits immediately $($at age $60)?(1$ mark$)$

b$)$ What is the PV of your CPP payments if you take them immediately? $(1$ mark$)$

c$)$ What is the PV at age $65$ of your CPP payments if you begin taking them at age $65?(1$ mark$)$

d$)$ What is the PV at age $60$ of your CPP payments if you begin taking them at age $65?(1$ mark$)$

e$)$ What is the PV at age $70$ of your CPP payments if you begin taking them at age $70?(1$ mark$)$

f$)$ What is the PV at age $60$ of your CPP payments if you begin taking them at age $70?(1$ mark$)$

g$)$ Out of the above three scenarios, what do you conclude is the best time to start taking your CPP benefits? Why? $(2$ marks$)$