Future Value and Present Value  Discussion
Mathematics

Tutor: None Selected  Time limit: 1 Day 
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?
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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.
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