William A. answered 06/02/15
Seasoned College Prof Tutoring Algebra, Pre-Calc, Stats and Finance
The question doesn't specify whether it wants the APR (annual percentage rate) or the EAIR (effective annual interest rate). I will give you both answers. What they are probably looking for is the APR.
4000 * (1+i)^(10*12) = 4491.73, where i is the monthly interest rate
Dividing both sides of the equation by 4000 gives us: (1+i)^120 = (4491.73/4000.00) = 1.122933
Taking the 120th root of both sides of the equation (using a calculator or Excel) gives us: 1+i = 1.122933^(1/120) = 1.000967. Subtracting 1 from both sides give us i = .000967 = .0967%.
That's the monthly interest rate, The APR is 12 times this value = 1.16%.
The EAIR is (1.000967)^12 -1 = 1.1662% (rounded = 1.17%).