Solve this problem MATHEMATICALLY not just the writings. Show every detail with formulas.

Jayce deposits $10,000 in Bank X on 1/1. Bank X credits interest at annual rate i = 15%. If Jayce decided to close his account, he'll receive simple interest up to the time of withdrawal. Jayce also visits Bank Y where he's told that he could open up an account anytime that year and receive /simple interest/ at annual rate i = 14.5%, paid from the date of deposit to 12/31.

Jayce is finding a way to maximize the return in his $10,000 over that year. Which one of the two choices, (a & b), would help hip to accomplish his goal?

a) Just leave his money in Bank X until 12/31. How much money will he be able to /withdraw/ on this day?

b) Jayce decides to pick a specific day to close his account at Bank X and immediately redeposit his fund in a new account in Bank Y. If this his ideal choice to accomplish his goal, what's the specific day and how much will he be able to withdraw from the Bank Y on 12/31?

Answer a and b

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STOP POSTING THE FOLLOWING ANSWER:

"

a) If Jayce keeps his money at Bank X until December 31 of this year, he will be able to withdraw $11,500 from the bank on that day.

b) If Jayce wanted to achieve his objective, the best option available to him would be to liquidate his account at Bank X on November 30 and immediately redeposit his funds in a new account with Bank Y. In this way, he would be able to withdraw $11,475 from Bank Y on December 31.

Please elaborate on your response.

The reason why it would be in Jayce's best interest to shut his account at Bank X on November 30 and immediately redeposit his money in a new account with Bank Y is due to the fact that doing so would result in the highest possible rate of return on his $10,000 throughout that calendar year. If Jayce did this, she would be able to collect interest at the higher rate of 14.5% for the entire year, rather than just 15% for the first month and then 14.5% for the rest of the year. This is because the higher rate would apply to the entire year. Because of this, the overall amount of interest earned would be higher, and as a consequence, so would the sum of money that Jayce would be able to withdraw from Bank Y on December 31."