The interest on an endowment of $120,000$ is left to beneficiary A for the first $15$ years, to beneficiary $B$ for the next $15$ years and to charity $C$ thereafter. If it is assumed that the endowment will earn a $4\%$ effective rate of interest, who gets the largest share?

$($a$)$ Beneficiary $A$

$($b$)$ Beneficiary B

$($c$)$ Charity C

A contractor pays $10,000$ at $t=0$ to purchase the land and $25,000$ at $t=\frac{1}{8}$ to purchase the materials to build a house. The house is then sold for $150,000$ at $t=\frac{3}{2}.$ The contractor also pays $90,000$ salary for the workers. If the the interest rate is $6\%$ effective, find the net present value of the whole project if the salary is paid continuously from $t=0$ until the sale.

$($a$)16448\mathrm{.}56$

$($b$)17950\mathrm{.}92$

$($c$)5518\mathrm{.}78$

$($d$)6194\mathrm{.}11$

What is the accumulated value of $2,000$ at the end of $5$ years if the nominal discount rate discounted quarterly is $d_4=8\%?$ Please round the amount to the nearest integer.