Natalia makes deposits in an account earning $6\%$ annual effective at the beginning of each quarter for $15$ years. Each quarterly

deposit in the first year is $200.$ Each quarterly deposit in the second year is $200+P,$ and the quarterly deposits in each year continue

to increase by $P$ for the $15$ year period.

At the end of $15$ years, Natalia will purchase a $20$ year annuity that makes continuous payments at a rate of $1,200$ per year for the first

$10$ years and $1,900$ per year for the second $10$ years. The interest rate on the continuous annuity is $4\%$ annual effective.

Calculate $P.$

$1\mathrm{.}97$

$2\mathrm{.}15$

$2\mathrm{.}58$

$2\mathrm{.}76$

$2\mathrm{.}95$