On March $1,2023,$ a company takes out a $15$

year loan of EUR $250,000$ at an interest rate of

$2\mathrm{.}4\%.$ The loan is repayable in constant monthly instalments of principal and interest.

a$)$What are the constant monthly instalments? $(1$

b$)$How much interest is payable on the $90$ th monthly instalment? $(1$

c$)$How much principal is repaid in the $45$ th monthly instalment? $(1$

d$)$The borrower has negotiated an early repayment clause $($without penalty$)$ on the outstanding capital. He wishes to use this clause just after the November $30,2029$ payment.How much of the outstanding principal must he repay? $(1$

e$)$What is the impact of inflation on this borrower? $(2$

Reminder$$The sum of a geometric se$$rie$,$ Sn with $1$ st term, u o $,$ multiplicative factor, r $,$ and number of terms,$$n is: Sn$=($ The nth power of r $-1)$ divided by $($r$-1)$