Question 1020861
The formula for the am future value, or the amount of an ordinary annuity is 

{{{A = R*( ( (1+r/n)^(nt) -1)/(r/n))}}}

Here, A = 157,532, R = 550, n = 12 (interest compounded monthly), t = 14 (years), and the unknown term is r, the annual interest rate.

==> {{{157532 = 550*( ( (1+r/12)^168 -1)/(r/12))}}} after substitution, and

==>23.86848485 = {{{((1+r/12)^168 -1)/r}}}   (Equation A)

after further simplification. 

There is no simple algebraic way of solving this equation for r, but by trial and error and using a scientific calculator, we can get quite close to the real value.

Now if r = 7%, the amount corresponding to the left-hand side of Eq'n. A is 23.669723.
If r = 7.2%, the amount corresponding to the left-hand side of Eq'n. A is 24.05381395.
the average of 7% and 7.2% is 7.1%, which gives 23.86, close to the real value of 23.86848485.
Therefore the annual interest rate rate is around 7.1%.