Using the compound interest principle, the best loan would be that with the lower return value, Hence, the best option is the option B. The amount saved by going for option B is $90.81
Using the compound interest formula :
Option A :
[tex] A = P(1 + \frac{r}{n})^{nt} [/tex]
[tex] A = 2000(1 + \frac{0.085}{4})^{4 \times 6} [/tex]
[tex] A = 2000(1 + \frac{0.085}{4})^{24} [/tex]
[tex] A = 2000(1 + 0.00708)^24[/tex]
[tex] A = 2000(1.6564) = 3312.83 [/tex]
Option B :
[tex] A = P(1 + \frac{r}{n})^{nt} [/tex]
[tex] A = 2000(1 + \frac{0.10}{1})^{1 \times 5} [/tex]
[tex] A = 2000(1 + 0.10)^{5} [/tex]
[tex] A = 2000(1 + 0.00708)^5[/tex]
[tex] A = 2000(1.61051) = 3257.79 [/tex]
Difference = 3312. 83 - 3221.02 = $90.81
The better loan would be option B ; as it is cheaper.
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