Question #9e9ef

1 Answer
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 + (PxxR)/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_"new" = A_"old" (1 + R/100)

Putting value of A_"old", we get,
A_"new" = P(1 + R/100)xx(1 + R/100)
A_"new" = P (1 + R/100)^2

Extending this for t time,

A = P (1 + R/100)^t

Here, we have to find R, so
P = 13000$
A = 20000$
t = 5 years

Putting this in A = P (1 + R/100)^t, we get

20000 = 13000 (1 + R/100)^5

20/13 = (1 + R/100)^5

Now we have to use a calculator. Calculate the 5^"th" root of 20/13

So it came out to be
1.08997

1.08997 = 1 + R/100

So, R comes out to be 8.997%

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