Donavan, now $24$ years old, started vaping at age $16,$ spending $$5$ per day on it until he turned $20.$ Hearing about the health risks of vaping, he switched to smoking filtered cigarettes on his $20$th birthday. This cost him $$20$ per day as he smoked one package per day. As of his $24$th birthday, he now smokes two packs a day costing him $$40$ daily and plans to continue smoking two packs daily until age $65.$ If$,$ instead, he had invested this daily amount over $49$ years with an average annual return of $7\%$ compounded monthly, how much would he have in his retirement plan? Assume $365$ days per year for compounding.

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Show calculations for the total savings had Donavan invested $(3$ marks$)$

Age $16($vaping$)$:

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Age $20($smoking one pack per day$)$:

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Age $24($smoking two packs per day$)$: Time Value:

FV $=$ Maturity value or Future value

$\backslash ($ P V$=\backslash )$ Principal or Present value

PMT $=$ Periodic annuity payments

$\backslash ($ n$=\backslash )$ Number of compounding periods per year

$\backslash ($ i$=\backslash )$ Annual interest rate

$\backslash ($ t$=\backslash )$ Time $($in years$)$

$\backslash ($ E Y$=\backslash )$ Effective yield TABLE F $-$ Time Value of Money Formulas