Question

SAMSUNG 18. The Biomedical Engineering (BME) Program is interested in purchasing a new scanning electron microscope (SEM). The cost of the microscope is P2,000,000; however, the prices have been dropping at the rate of about 5% per year. The program can set aside about P320,000 annually into an account that will accrue interest at 10%. How long will it be before BME can purchase the microscope?

Answer 1

Let us first consider that the cost of microscope remains the same i.e there is no drop in the price each year. With a constant cost of microscope, the number of years it takes to accumulate 2,000,000 if 320,000 is set aside annually is found as

1320,000[(1+0.10) -1] 2,000,000 = 0.10

(1+0.10)ⁿ - 1 = 0.625

n ln 1.10 = ln 1.625

n = 5.1 years

At a constant price of 2,000,000, we need 5.1 years if we deposit 320,000 each year.

The price of the microscope decreases by 5% each year, hence in 5.1 years, the price of the microscope will be

Price in 5 years = 2,000,000 $\times$ ( 1 - 0.05 ) ^5.1

Price in 5 years = 1,539,644.24

To accumulate 2,000,000 , we need 5.1 years , hence to accumulate 1,539,644.24 , years required

Years needed = ( 1,539,644.24 $\times$ 5.1) $\div$ 2,000,000

Years needed = 3.93 years .

BME can purchase the microscope in 3.93 years.