Question 1044475
p = principal
r = interest rate


simple interest for 1 year equation is pr = 50


compound interest equation for 2 years is p * (1+r)^2 - p = 102


simplify p * (1+r)^2 - p = 102 to get:


p + 2pr + pr^2 - p = 102


since plus p and minus p cancel out, you are left with:


2pr + pr^2 = 102


solve for p in pr = 50 to get p = 50/r


replace p with 50/r in 2pr + pr^2 = 102 to get:


2*50/r*r + 50/r*r^2 = 102


simplify to get 100 + 50r = 102


subtract 100 from both sides of the equation to get 50r = 2


divide both sides of the equation by 50 to get r = 2/50


r = 2/50 is the same as r = .04


now that you know r, you can solve for p.


pr = 50 becomes p * .04 = 50 


solve for p to get p = 50/.04 = 1250


p * (1+r)^2 - p = 102 becomes 1250 * (1.04)^2 - 1250 = 102 which becomes 102 = 102


solution is good.


p = 1250
r = .04