Thank you for the opportunity to help you with your question!
a) Simple Interest = Principal ($6000) * Time (0.5 years) * Rate of interest (0.12) = $360
b) Let n = no. of times interest is compounded per year = 12 (as it is compounded monthly)
Compount Interest = Principal* (1 + Rate/n)^n*t - Principal
= 6000(1 + 0.12/12) ^ 12*0.5 - 6000
= 6000(1.01)^6 - 6000 = 6369.12 - 6000 = $369.12
Therefore, simple interest method yields lower amount at the end of 6 months.
The two methods differ in how the interest is calculated as illustrated by the above formulas. If one is investing for a longer period of time, compound interest yields higher returns.Please let me know if you need any clarification. I'm always happy to answer your questions.
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