EXERCISE III $(5$ points$)$

Mr$.$ DAVIS wants to replace his car in $3$ years' time. To this end, he opens a savings account on $23$ March $2022$ with an effective$/$actuarial annual rate of $4\mathrm{.}25\%.$ His first payment is made on $23$ April $2022.$ Capitalization is monthly.

a$)$ Calculate the monthly payment, a$,$ that Mr$.$ DAVIS must make to this account if he wishes to have EUR $20,000$ available on $23$ March $2023.$

Mr$.$ Davis does not want to save more than EUR $490$ per month. In order to achieve his goal while still meeting the deadlines, he is looking for a more profitable investment.

b$)$ What impact could this decision have on the interest rate of the investment, so that Mr$.$ Davis receives a capital of EUR $20,000?$