# Question 9e9ef

May 11, 2016

8.997%

#### Explanation:

I am assuming the amount is compounded annually.

Note:- In this explanation, A is amount, P in Principal amount, R is rate of interest, and t is the time

Suppose I have $P$ $. Now if the amount is compounded annually, then After first year, $A = P + \frac{P \times R}{100}$, where $R$is the rate of interest. After second year, the rate of interest in on the CURRENT amount, not the original amount, so the previous A becomes the new P A_"new" = A_"old" + (A_"old" xx R)/100# ${A}_{\text{new" = A_"old}} \left(1 + \frac{R}{100}\right)$Putting value of ${A}_{\text{old}}$, we get, ${A}_{\text{new}} = P \left(1 + \frac{R}{100}\right) \times \left(1 + \frac{R}{100}\right)$${A}_{\text{new}} = P {\left(1 + \frac{R}{100}\right)}^{2}$Extending this for $t$time, $A = P {\left(1 + \frac{R}{100}\right)}^{t}$Here, we have to find $R$, so P = 13000$
A = 20000$t = 5 years Putting this in $A = P {\left(1 + \frac{R}{100}\right)}^{t}$, we get $20000 = 13000 {\left(1 + \frac{R}{100}\right)}^{5}$$\frac{20}{13} = {\left(1 + \frac{R}{100}\right)}^{5}$Now we have to use a calculator. Calculate the ${5}^{\text{th}}$root of $\frac{20}{13}$So it came out to be $1.08997$$1.08997 = 1 + \frac{R}{100}\$

So, R comes out to be 8.997%

P.S. Round it off as per your requirements.