Answer:
The interest rate is 3.79% or 3.8%
Step-by-step explanation:
The formula to find how much money A we have at the end of t years if we start with a principal or amount of money P today and the interest is compounded n times in the years is:
A=P(1+ r/n)^(nt) (1)
Here A = $2,976.45 the final amount
t = 11 years
P = $1,963.45.
and n = 4 because the interest is compounded quarterly or 4 times in the year.
We the need to simplify the interest rate r in (1) so:
A=P(1+ r/n)^(nt) (1)
A/P = (1+ r/n)^(nt)
(A/P)^(1/nt) = (1+ r/n)
(A/P)^(1/nt) - 1 = r/n
((A/P)^(1/nt) - 1 ) * n = r
r = ((A/P)^(1/nt) - 1 ) * n
We replace values and solve doing parenthesis exponents first
r = ((2,976.45/1,963.45.)^(1/(4*11)) - 1 ) * 4
r= ((1.51^(1/44)) -1)*4
((1.51^(1/44)) -1)*4
r= (1.009499443 - 1)*4
r= 0.009499443 *4 = 0.037997773
That expressed in percentage multiplying by 100 is 3.79% or 3.8% interest
