Mr. Cruz

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

Correct answer:

a =  34300 eur
b =  32400 eur

Step-by-step explanation:

$$\begin{gathered} x=21600\text{eur} \\ n=3 \\ p=16\frac{2}{3}=16+\frac{2}{3}=\frac{16\cdot 3+2}{3}=\frac{50}{3}\doteq 16.6667\% \\ r=100\%+p\%=1+\frac{p}{100}=1.1666666666667 \\ a=x\cdot r^n=x\cdot {\frac{7}{6}}^n=21600\cdot 1.1667^3=34300\text{eur} \end{gathered}$$

$$\begin{gathered} r_1=p\%=\frac{p}{100}=0.16666666666667 \\ i=x\cdot r_1=x\cdot \frac{1}{6}=21600\cdot 0.1667=3600 \\ b=x+n\cdot i=21600+3\cdot 3600=32400=32400\text{eur} \\ a>b \\ \Delta =a-b=34300-32400=1900\text{eur} \end{gathered}$$

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