Please explain this question and provide a solution

Sample Q: Pournima receives an invoice for $$17,500$ with terms of $5/10$ net

$30.$

a$)$ What is the discounted amount she would have to pay, and on what day

would she pay it$,$ to settle the debt early?

b$)$ If she doesn$$t pay the discount amount on day $10$ but instead waits until

day $30$ to pay the full amount, what simple interest rate is she paying?

A: As we will see, it is often very useful in this course to draw a timeline of

payments!

a$)$ The terms $5/10$ net $30$ mean she gets a d $=5\%$ discount if she pays on

$($or before$)$ day $10.$ So the discount amount D $=$ F $5\%$F $=$ F $(1$ d$)=$

$16,625\mathrm{.}00.$

b$)$ Depends on the daycount convention! If she doesn$$t pay early, then

effectively she is borrowing A$(0)=$ D $=$ $$16,625\mathrm{.}00$ on day $10$ and will pay

A$($T$)=$ F $=$ $$17,500$ on day $30.$ Also T in days is $30-10=20,$ but we

need to know the daycount convention to convert T to years. Suppose the

daycount convention is ACT $/360,$ then T $=20/360=0\mathrm{.}05556$ and

i $=($A$($T$)/$A$(0)1)/$T $=(17,500/16,6251)/0\mathrm{.}05556=0\mathrm{.}94729=94\mathrm{.}729\%(!)$

Obviously, Pournima is highly motivated to pay the discounted amount on

day $10.$ In fact, if she has a line of credit with the bank at a lower interest

rate, she should borrow from the bank $($on day $10)$ to pay the invoice, and

then pay off the LOC with the bank on day $30.$ This would be cheaper for

her than simple waiting until day $30$ to pay her supplier. So let$$s add parts

c$)$ and d$)$ to our question above:

Q: c$)$ Pournima has a line of credit from her bank that charges her $30\%$

annual simple interest. $($In the real world, a bank line of credit charges daily

compound interest but we$$re not there yet!$)$ How much would she owe the

bank on day $30$ if she borrowed the discounted amount D on day $10($and

used it to settle the invoice$)?($Use the same daycount convention as you

used for the invoice.$)$

d$)$ How much money would she save by doing this $($compared to just waiting

until day $30$ to pay the invoice$)?$

A:

c$)$ The bank loan is for $20$ days with A$(0)=16,625,$ T $=20/360=0\mathrm{.}05556,$

i $=30\%=0\mathrm{.}30$ so

$6$

A$($T$)=$ A$(0)(1+$ iT$)=16,902\mathrm{.}08$

d$)$ If she borrows from the bank on day $10$ to settle the invoice, instead of

owing her supplier $$17,500$ she will owe the bank $$16,902\mathrm{.}08$ a savings of

$$597\mathrm{.}92.$