Graph the timeline and calculate the value equations for the following problems:

a$.$ An investment company received a note earning $6\%$ interest for $$230,000$ on March $20$ for $120$ days. On June $25$ of the same year, he offered it to another investment company that wanted to earn $7\%.$ How much does the investment company receive for the first promissory note? $($date June $25).$

b$.$ A person wants to settle an account for $$16,000$ in $5$ months with $6\%$ interest. To do this, you are proposing to pay $$5,000$ today and the rest in $2$ equal payments within $6$ and $8$ months. How much will the payments be if the interest rate is $7\mathrm{.}5\%?($Focal date month $6).$

c$.$ What is the value of an invoice for $$38,150$ that has the following terms of sale: $4/10,$ n$/30?$ Also determine the annualized opportunity cost.

d$.$ Calculate the simple and compound interest that