The loan of 30.000 euros is depriciated after 10 years, with equal annuities and interest of 11% of annual capitalization. how can the annuity be determined? -this one seems to be the toughest of them all for me.
annuities and interest
1 Answers
You haven't told us what any of the words mean, so I'm going to make some guesses.
You start with 30000, pay out an annuity $A$, so you have $30000-A$, then credit 11% interest, so you have $(30000-A)(1.11)=(30000)(1.11)-1.11A$ Then, you pay out $A$ again, and again credit 11%, so you have $((30000-A)(1.11)-A)(1.11)=30000(1.11)^2-(1.11)^2A-1.11A$ Now you do it again, getting $30000(1.11)^3-((1.11)^3+(1.11)^2+1.11)A$ After 10 of these episodes, everything's gone. So you want $30000(1.11)^{10}-((1.11)^{10}+(1.11)^9+\cdots+1.11)A=0$ Now you can solve this for $A$.
EDIT: If you credit interest before paying annuity, the calculations look like $1.11P-A,\quad1.11^2P-1.11A-A,\quad1.11^3P-1.11^2A-1.11A-A,\dots$ where $P=30000$, and you wind up with $1.11^{10}P-(1.11^9+1.11^8+\cdots+1)A=0$ to solve for $A$.