Question $8\mathrm{.}02$

An annuity pays $50$ in $6$ months, $55$ in $1\mathrm{.}5$ years, $60$ in $2\mathrm{.}5$ years, and so on until a final

payment of $150$ in $20\mathrm{.}5$ years.

The annual effective interest rate is $5\%.$

Calculate the present value of the annuity.

A $1,141\mathrm{.}21$

B $1,169\mathrm{.}39$

C $1,198\mathrm{.}27$

D $1,227\mathrm{.}86$

E $3,409\mathrm{.}96$

Please solve by hand. The answer should be $1,198\mathrm{.}27$ but I don't know how to get there without calculating all values individually and adding. There should be one equation that does it completely.