SOLUTION: The simple interest on a sum of money in one year is N$50 and compound interest in two years is N$102. Find the sum of money and the rate of interest.

Question 1044475: The simple interest on a sum of money in one year is N$50 and compound interest in two years is N$102. Find the sum of money and the rate of interest.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
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

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