Question 1096881
<br>The formula for the value P of an annuity with regular deposits of amount A, n times per year for t years, at an annual interest rate of r, is<br>
{{{P = A((1+r/n)^(nt)-1)/(r/n)}}}<br>
In your problem, we know A is 650, n is 12, and t is 14; we need to find r.  The formula is<br>
{{{154986 = 650((1+r/12)^(12*14)-1)/(r/12)}}}<br>
If you know the interest rate r and 3 of the other 4 numbers, you can calculate the missing number using the formula, or some form of it.  But the interest rate r occurs in two different places in the formula, making it impossible to do a direct calculation to find the interest rate, if it is the unknown in the problem.<br>
So all you can do is use some mathematical tool, like a graphing calculator, to find the answer.  I used my TI-84 calculator to graph the two functions
{{{154986}}} and {{{650((1+x)^(12*14)-1)/(x)}}}
and used the intersection of the two graphs to find the monthly interest rate is 0.00398 = 0.398%, making the annual interest rate 0.04776 = 4.776%.