The Formula for the compound interest is:
[tex]A=P(1+ \frac{r}{n})^{n*t} [/tex]
A = Amount Accumulated = $5000
P = Principal Amount = $1250
n = compound period in a year = 4
r = Interest Rate
t = Time in years = 12
Using the values in the formula, we get:
[tex]5000=1250(1+ \frac{r}{4})^{4*12} \\ \\
\frac{5000}{1250} =(1+0.25r)^{48} \\ \\
4=(1+0.25r)^{48} \\ \\
1+0.25r=1.0293 \\ \\
0.25r=0.0293 \\ \\
r=0.1172
[/tex]
Thus, in order to achieve the given conditions, 11.72% interest rate is required.
