Mr. Cruz

Mr. Cruz borrowed 21,600 euros for three years at 16 2⁄3% compounded annually. At the same time, Mr. Santos borrowed the same Amount at Simple Interest for the same period and at the same interest rate. Who Pays more and how much?

Correct answer:

a =  34300 eur
b =  32400 eur

Step-by-step explanation:

$$\begin{gathered} x=21600\text{eur} \\ n=3 \\ p=16\frac{2}{3}=16+\frac{2}{3}=\frac{16\cdot 3+2}{3}=\frac{48+2}{3}=\frac{50}{3}\doteq 16.6667\% \\ r=100\%+p\%=1+\frac{p}{100}=1.1666666666667 \\ a=x\cdot r^n=21600\cdot {\frac{7}{6}}^3=34300\text{eur} \end{gathered}$$

$$\begin{gathered} r_1=p\%=\frac{p}{100}=\frac{16.666666666667}{100}=0.16666666666667 \\ i=x\cdot r_1=21600\cdot \frac{1}{6}=\frac{21600\cdot 1}{6}=\frac{21600}{6}=3600 \\ b=x+n\cdot i=21600+3\cdot 3600=32400=32400\text{eur} \\ a>b \\ \Delta =a-b=34300-32400=1900\text{eur} \end{gathered}$$

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