Future Value and Present Value - Discussion

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Compound Interest Value

Question 1:

Explain which of the two options below results in a lower balance after 6 months on an investment of $6,000.

  • Annual simple interest of 12% applied at the end of 6 months.
  • A monthly interest rate of 1% applied at the end of each month and before the start of the next month. (Compound interest at 12% per year, compounded monthly.)

Discuss why the two methods result in different results.

In what circumstances might you select one option over another?

Sep 24th, 2015

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.
Sep 24th, 2015

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