Dana and Ricardo, two classmates at a college, decided to use their free time after classes to create mobile apps. On October $07,2019,$ they received a loan of $$3000$ from a bank at $8\mathrm{.}5\%$ p$.$a$.$ to start their small business. Two months later, they launched their first app in the community, and it was highly successful. On March $02,2019,$ a larger tech company paid them $$50,000$ to purchase rights to their app. Dana and Ricardo used $$5000$ from this amount to settle the bank loan and to cover other miscellaneous expenses.e

They then shared the balance of $$45,000$ equally between themselves.

Dana invested a portion of it in a $182-$day T$-$bill that had an interest rate of $4\%$ p$.$a$.$ and a face value of $$7500$ and used the balance in a $270-$day interest$-$bearing promissory note at $6\%$ p$.$a$.$

Ricardo, on the other hand, invested a portion of it in a $270-$day non$-$interest$-$bearing promissory note that had an interest rate of $5\%$ p$.$a$.$ and a face value of $$9000,$ and loaned the balance to his friend, who was running a successful website$-$design business, for $182$ days.

Dana and Ricardo, two classmates at a college, decided to use their free time after classes to create mobile apps. On October $07,2019,$ they received a loan of $$3000$ from a bank at $8\mathrm{.}5\%$ p$.$a$.$ to start their small business. Two months later, they launched their first app in the community, and it was highly successful. On March $02,2019,$ a larger tech company paid them $$50,000$ to purchase rights to their app. Dana and Ricardo used $$5000$ from this amount to settle the bank loan and to cover other miscellaneous expenses.

They then shared the balance of $$45,000$ equally between themselves.

Dana invested a portion of it in a $182-$day T$-$bill that had an interest rate of $4\%$ p$.$a$.$ and a face value of $$7500$ and used the balance in a $270-$day interest$-$bearing promissory note at $6\%$ p$.$a$.$

Ricardo, on the other hand, invested a portion of it in a $270-$day non$-$interest$-$bearing promissory note that had an interest rate of $5\%$ p$.$a$.$ and a face value of $$9000,$ and loaned the balance to his friend, who was running a successful website$-$design business, for $182$ days.

question $(1)$ Ricardo wants have the same amount as Dana in $182$ days. and dana had $23,074\mathrm{.}85$ after $182$ days. If he discounts his non$-$interest$-$bearing promissory note at $7\%$ p$.$a$.$ what interest rate should he charge his friend for the loan? prepare a nice detailed and neat time line first then solve the question. please don't forget to prepare the time line first it's mandatory.