Compound interest can be defined as the interest <em>on a deposited amount, an investment</em> that is <em>compounded based on its principal and interest rate.</em>
It will take about 3.239 years for the principal amount of $13,000 to double its initial value.
From the above question, we can deduce that we are to find the time "t"
The formula to find the time "t" in compound interest is given as:
t = ln(A/P) / r
where:
P = Principal = $13,000
R = Interest rate = 21.4%
A = Accumulated or final amount
From the question, the Amount "A" is said to be the double of the principla.
Hence,
A = $13,000 x 2
= $26,000
- Step 1: First, convert R as a percent to r as a decimal
r = R/100
r = 21.4/100
r = 0.214 per year.
- Step 2: Solve the equation for t
t = ln(A/P) / r
t = ln(26,000.00/13,000.00) / 0.214
t = 3.239 years
Therefore, it will take about 3.239 years for the principal amount of $13,000 to double its initial value.
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