Answer:
≈ 20 years
Explanation:
so we take the equation, A=P(1+ r/n)^nt and plug in the appropriate values:
A = resulting value, so we plug in the "resulting value" from this equation = 1900+900, because the principal (starting) amount + the interest that we collected
P= the principal amount. this is the starting amount, the amount we deposit - $1900.
r = this is the rate at which our interest is compounded. it says 2%, but we have to change this to a decimal to use it in our function. this is easy, we just move the decimal point two places to the left = 0.02
n = n is the amount of times it is compounded per year. It says compounded "quarterly", so we can put 4 for n. notice how it says n in both places? in both places we can put 4
t = t is the amount of years that this interest is collected. this is what we need to solve for. we will use x for this.
our resulting equation → 2800 = 1900(1 + 0.02/4)^4x
all we have to do now is solve for x.
we start by simplifying the 1 + 0.02/4. simply, this equals 1.005.
we are left with 1900(1.005)^4x = 2800
then, we divide both sides by 1900.
this results in (1.005)^4x = 2800/1900
simplifying the fraction, we get 28/19
now, we separate the 4x using exponent rules
(1.005^4)^x
taking 1.005^4, we get 1.02.
so we are left with 1.02^x=28/19
now, to simplify this equation, we have to turn to logarithmic functions.
converting the exponential equation to a logarithmic equation, we get log_{1.02}(28/19) = x
punching this into a calculator, we get ≈ 20 years.
I hope this helps... :)