Answer:
Step-by-step explanation:
Factorise numerator and denominator
x² - 9 ← is a difference of squares and factors in general as
a² - b² = (a - b)(a + b) , then
x² - 9
= x² - 3² = (x - 3)(x + 3)
x² - 3x ← factor out x from each term
= x(x - 3)
Then
= ← cancel common factor (x - 3) on numerator/denominator
=
The time taken if the interest is compounded quarterly will be 21.212 years or about 21 years 3 months.
We have,
Principal = 2900,
Amount = 25,600
And,
Rate of Compounded Interest = 10.4%
According to the question,
Interest is compounded quarterly,
So,
Rate of Compounded Interest = = 2.6%
Now,
Using the Compound Interest formula,
i.e.
A = P(1 +
i.e.
25600 = 2900(1 +
On solving we get,
= (
On solving further,
t =
On solving for log,
We get,
t = 21.212 years or about 21 years 3 months
Hence, we can say that the time taken if the interest is compounded quarterly will be 21.212 years or about 21 years 3 months.
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