According to the <em>compound interest</em> model, we find the following results: I) x ≈ 11.5 yr, C' = $ 101317.36, II) r ≈ 7.4 %, x ≈ 9.8 yr, III) C = $ 7626.38, x ≈ 8.6 yr, IV) r ≈ 6.5 %, C = $ 12801.61
<h3>How to determined all the variables associated with compound interest</h3>
<em>Compound</em> interest describes the <em>capital</em> gain in term of <em>deposited</em> capital and the consideration that such capital is increased continuously in time. The compound interest model is shown below:
C' = C · (1 + r/100)ˣ (1)
Where:
- C - Initial capital
- C' - Current capital
- r - Interest rate, in percentage.
- t - Time, in years
The <em>doubling</em> time (x) is the period needed for a capital to be doubled. It is described by the following expression based on (1):
x = (㏒ 2)/[㏒ (1 + r/100)] (2)
Now we proceed to calculate each missing variable:
Case I - Doubling time
x = (㏒ 2)/[㏒ (1 + 6.2/100)]
x ≈ 11.5
Case I - Current capital
C' = 75000 · (1 + 6.2/100)⁵
C' = 101317.36
Case II - Interest rate
r ≈ 7.4
Case II - Doubling time
x = (㏒ 2)/[㏒ (1 + 7.3/100)]
x ≈ 9.8
Case III - Initial capital
C = 11414.71/(1 + 8.4/100)⁵
C = 7626.38
Case III - Doubling time
x = (㏒ 2)/[㏒ (1 + 8.4/100)]
x ≈ 8.6
Case IV - Interest rate
r ≈ 6.5
Case IV - Initial capital
C = 17539.32/(1 + 6.5/100)⁵
C = 12801.61
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