Factors that increase costs and prices—especially for materials and manufacturing costs sensitive to market, technology, and labor availability—can be considered separately using the real interest rate, i, the inflation rate, f, and additional increases that grow at a geometric rate, g (commonly due to maintenance and repair cost increases as machinery ages). The future amount is calculated based on a current estimate by using the relation: F = P(1 + i)n (1 + f )n (1 + g)n = P[(1 + i) (1 + f ) (1 + g)]n The current cost to manufacture an electronic subcomponent is $145,000 per year. Provided the average annual rates for i, f, and g are 8%, 4%, and 3%, respectively, determine the equivalent future cost (a) in 3 years, and (b) in 8 years.

Factors that increase costs and prices—especially
for materials and manufacturing costs sensitive to
market, technology, and labor availability—can be
considered separately using the real interest rate, i,
the inflation rate, f, and additional increases that
grow at a geometric rate, g (commonly due to
maintenance and repair cost increases as machinery
ages). The future amount is calculated based
on a current estimate by using the relation:
F = P(1 + i)n (1 + f )n (1 + g)n = P[(1 + i) (1 + f ) (1 + g)]n
The current cost to manufacture an electronic subcomponent
is $145,000 per year. Provided the average
annual rates for i, f, and g are 8%, 4%, and
3%, respectively, determine the equivalent future
cost (a) in 3 years, and (b) in 8 years.