10.3% compounded quarterly.
The formula for compound interest is
A = P(1+I/N)^TN
where
A = Amount after interest is granted
P = Principle
I = Interest rate
N = Number of periods per year
T = Number of year
Since we want to get 1500 with an starting principle of 1000, that means that (1+I/N)^TN has to equal 1.5. And since we know that TN will be 4 * 4 or 16, we know that (1+I/N) has to be the 16th root of 1.5, so let's calculate
10^(log(1.5)/16) = 10^(0.176091259/16) = 10^0.011005704 = 1.025665396
Now write the expression
1 + I/4 = 1.025665396
And solve for I
1 + I/4 = 1.025665396
I/4 = 0.025665396
I = 0.102661586
So the desired interest rate will be 10.3% compounded quarterly.
