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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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Answer:
Either
(approximately
) or
(approximately
.)
Step-by-step explanation:
Let
denote the first term of this geometric series, and let
denote the common ratio of this geometric series.
The first five terms of this series would be:
First equation:
.
Second equation:
.
Rewrite and simplify the first equation.
.
Therefore, the first equation becomes:
..
Similarly, rewrite and simplify the second equation:
.
Therefore, the second equation becomes:
.
Take the quotient between these two equations:
.
Simplify and solve for
:
.
.
Either
or
.
Assume that
. Substitute back to either of the two original equations to show that
.
Calculate the sum of the first five terms:
.
Similarly, assume that
. Substitute back to either of the two original equations to show that
.
Calculate the sum of the first five terms:
.