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

40%.

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+(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+(r)/(1))^(1*2)`

`196=100(1+r)^(2)`

`(196)/(100)=(100(1+r)^(2))/(100)\\\\1.96=(1+r)^2`

`(1+r)^2=1.96`

Take positive square root of both sides:

`√((1+r)^2)=√(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* 100\%=40\%`

Therefore, the interest rate was 40%.