Respuesta :
Answer:
40%.
Step-by-step explanation:
We have been given that an amount of $100 compounded annually is increased to $196 in 2 years. We are asked to find the interest rate.
We will use compound interest formula to solve our given problem.
[tex]A=P(1+\frac{r}{n})^{nt}[/tex], where,
A = Final amount,
P = Principal amount,
r = Annual interest rate in decimal form,
n = Number of times interest is compounded per year,
t = Time in years.
Upon substituting our given values in above formula, we will get:
[tex]196=100(1+\frac{r}{1})^{1*2}[/tex]
[tex]196=100(1+r)^{2}[/tex]
[tex]\frac{196}{100}=\frac{100(1+r)^{2}}{100}\\\\1.96=(1+r)^2[/tex]
[tex](1+r)^2=1.96[/tex]
Take positive square root of both sides:
[tex]\sqrt{(1+r)^2}=\sqrt{1.96}[/tex]
[tex]1+r=1.4\\\\1-1+r=1.4-1\\\\r=0.4[/tex]
Since interest rate is in decimal, form, so we will convert it into percentage as:
[tex]0.4\times 100\%=40\%[/tex]
Therefore, the interest rate was 40%.
