Question

Question #9e9ef

Answer 1

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.