EXERCISE VII $(4$ points$)$

An individual takes out a loan of EUR $300,000$ for $10$ years at a rate of $3\%.$ This loan is contracted on October $12$th $2023,$ it is repayable in constant monthly instalments of principal and interest. The first repayment is due on November $12$th$,2023.$

a$)$What is the amount of the constant monthly repayments? $($use the proportional rate$)$

b$)$What is the interest charge on the $50$th payment?

c$)$What is the capital repaid in the $30$th payment?

d$)$The loan shall include a clause for the early repayment, without penalty, of the outstanding principal. The individual wishes to use this clause after the payment on $31$ December $2025,$ how much outstanding capital does he have to repay?