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We want to convert this equation in terms of m, where
While solving this problem, I instantly noticed the in the first term of the equation. Replace that with m.
Simplifying the rest is not as obvious. Using the distributive property, we can change to
Do you see the "m" in here? Look again if you don't.
Now we can simplify the equation to and this cannot be simplified further.
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<h3>What would be the value of $150 after eight years if you earn 12 % interest per year? A. $371.39 B. $415.96 C. $465.88 </h3>
<em>The compound interest is applied, that is to say, each year the interest produced is accumulated to the outstanding capital and the interest of the next period is calculated on the new outstanding capital.</em>
The formula for calculating compound interest is:
Compound interest = Total amount of Principal and interest in future less Principal amount at present = [P(1 + i)ⁿ] – P
(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods)
[P(1 + i)ⁿ] – P = P[(1 + i)ⁿ – 1] = $150[(1 + 12/100)⁸ – 1] = $150[(1.12)⁸ – 1] = $150[2.47596317629 - 1] = $150[1.47596317629] = $221.39
Total amount = $150 + $221.39 = $371.39
Answer : A.) $371.39