Question $16$

Peter is $14$ years away from retirement and expects to live for $20$ years after retirement. Peter plans to move to a retirement home immediately after retirement. Currently, a retirement home costs $$40,000$ per year, payable at the beginning of the year. Peter expects this annual cost to increase by $3\%$ per year. How much does Peter need to have in the bank when he retires $($just before paying for the first year at the retirement home$)$ to cover the $20$ years that he expects to live in the retirement home if the interest rate on the account is $3\%$ per year?

a$.$ $$1,220,072$

b$.$ $$1,210,072$

c$.$ $$1,230,072$

d$.$ $$1,200,072$

e$.$ $$1,240,072$