Loan interest periods

The bank provides loans with an interest rate of 5% pa. How much interest will you pay if you borrow 5,000 euros for:
A) 1 year

B) 1/2 year

C) 1/4 year

D) 5 years?

Final Answer:

a =  255.81 eur
b =  126.31 eur
c =  62.76 eur
d =  1416.79 eur

Step-by-step explanation:

$$\begin{gathered} x=5000\text{eur} \\ r=5\%=\frac{5}{100}=\frac{1}{20}=0.05 \\ q=1+r/12=1+0.05/12=\frac{241}{240}\doteq 1.0042 \\ a=x\cdot q^{12}-x=5000\cdot 1.0042^{12}-5000=255.81\text{eur} \end{gathered}$$

$b=x\cdot q^6-x=5000\cdot 1.0042^6-5000=126.31\text{eur}$

$c=x\cdot q^3-x=5000\cdot 1.0042^3-5000=62.76\text{eur}$

$d=x\cdot q^{5\cdot 12}-x=5000\cdot 1.0042^{5\cdot 12}-5000=1416.79\text{eur}$

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