Question

What was the interest rate if your balance on an investment of $857 at the end of six years is $1268.36

Answer 1

Answer:

The rate of interest is 9.5092%  

Step-by-step explanation:

Given as :

The investment amount = p = $857

The Amount after 6 years = A = $1268.36

The time period = t = 6 years

Let The rate of interest = r%

Now, From Compound Interest method

Amount = Principle × $(1+\dfrac{\textrm rate}{100})^{\textrm time}$

Or, A = p × $(1+\dfrac{\textrm r}{100})^{\textrm t}$

Or, $1268.36 = $857 × $(1+\dfrac{\textrm r}{100})^{\textrm 6}$

Or, $\dfrac{1268.36}{857}$ =  $(1+\dfrac{\textrm r}{100})^{\textrm 6}$

Or, 1.48 =  $(1+\dfrac{\textrm r}{100})^{\textrm 6}$

Taking power $\dfrac{1}{6}$  both side

So, $1.48^{\frac{1}{6}}$ = $((1+\dfrac{r}{100})^{6})^{\frac{1}{6}}$

Or, 10.5092 = 1 + $\dfrac{r}{100}$

Or, 10.5092 - 1 = $\dfrac{r}{100}$

Or, 9.5092 = $\dfrac{r}{100}$

∴   r % = 9.5092

So , The rate of interest = r = 9.5092 %

Hence, The rate of interest is 9.5092%   Answer