Annual interest

A loan of 10 000 euros is to be repaid in annual payments over ten years. Assuming a fixed 10% annual interest rate compounded annually, calculate:

(a) the amount of each annual repayment
(b) the total interest paid.

Correct answer:

a =  1627.45 Eur
i =  6274.54 Eur

Step-by-step explanation:

$$\begin{gathered} l=10000\text{eur} \\ r=10\%=\frac{10}{100}=\frac{1}{10}=0.1 \\ n=10 \\ q=(1+r{)}^n=(1+\frac{1}{10}{)}^{10}\doteq 2.5937 \\ a=l\cdot \frac{r\cdot q}{q-1}=10000\cdot \frac{0.1\cdot 2.5937}{2.5937-1}=1627.45\text{Eur} \end{gathered}$$

$i=n\cdot a-l=10\cdot 1627.4539-10000=6274.54\text{Eur}$

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