Question #9e9ef

1 Answer
May 11, 2016

Answer:

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.