Question

At the end of 2​ years, P dollars invested at an interest rate r compounded annually increases to an​ amount, A​ dollars, given by the following formula. Upper A equals Upper P (1 plus r )squared Find the interest rate if ​$100 increased to ​$196 in 2 years. Write your answer as a percent.

Answer 1

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.

$A=P(1+\frac{r}{n})^{nt}$, 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:

$196=100(1+\frac{r}{1})^{1*2}$

$196=100(1+r)^{2}$

$\frac{196}{100}=\frac{100(1+r)^{2}}{100}\\\\1.96=(1+r)^2$

$(1+r)^2=1.96$

Take positive square root of both sides:

$\sqrt{(1+r)^2}=\sqrt{1.96}$

$1+r=1.4\\\\1-1+r=1.4-1\\\\r=0.4$

Since interest rate is in decimal, form, so we will convert it into percentage as:

$0.4\times 100\%=40\%$

Therefore, the interest rate was 40%.