The engineering company decided to buy a machine that serve $13$ years. The company must pay a monthly payment of $$3251$ for $3$ years starting at the end of year $5.$ The company made an initial payment of $$25,000$ at the beginning of year $1.$ The interest rate is $5\%$ per month. The present worth equals:

Select one:

a$.$ $$3,023\mathrm{.}87$

b$.$ $$56,483\mathrm{.}51$

c$.$ $$2,879\mathrm{.}88$

d$.$ $$53,793\mathrm{.}81$