TOPIC:Uniform Arithmetic Gradient and Uniform Geometric Gradient

ENGINEERING ECONOMICS 1.An employee was promised by his boss that he will have a salary of P295,000 on his rst month and will be increased by 30.7% on the succeeding months. What will be his total salary for one year if interest is 24% compounded annually. 2. A certain amount was borrowed today and to be paid for 5 years. The rst payment was P310300 made at the end ot the rst year and the succeeding payments to be increased by P30,500 per year. How much is the borrowed amount? UNIFORM ARITHMETIC GRADIENT - a series of payments that increases or decreases in each succeeding periods by a constant amount, G. P K 0 4 n-1 A A+ G+ A+ 2G A+ 3G A+ (n-2) G -A+ (n-1)G P = A (1 + i)n - 1 n i(1 + i)n $ 7 G (1 + i)n - 1 i(1 + i)n (1 + i)n F = A [(1 + 1)" - 1] G (1 + i)" - 1 - -n Take Note: for the +, (+) if payment is increasing and (-) if payment is decreasingUNIFORM GEOMETRIC GRADIENT a series of payments that increases or decreases in each succeeding periods by a constant rate, Is. P K 0 n-1 A A(1+ [g) A(1+ r) 2 A(1+ rg) 3 A(1+ r) (1-2) T1 4 A(1+ rg) (n-1) Let: 1+rg W= 1+i If: w# 1 (r# i), then A - wh P = 1+i 1 - W If: w = 1 (r = i), then An P = 1+i F = P(1+ i)"