Question

True or False and why:

A) With continuous compounding at an interest rate of 5%, an investment of $100 will be less than $115 after three years.

B) The capitalized cost for an air filter that costs $25 that needs to be bought every year is more than $200 if we one uses a monthly interest rate of 1%.

Answer 1

A) As per the information provided in the question

Rate on interest i =5% per annum

Period (N) = 3 years

Investment is = $100

Future value of the investment = $100 (F/P, i , N)

Future value of the investment = $100 (F/P, 5% , 3)

Future value of the investment = $100 (1.1576)

Future value of the investment = $115.76

Though the future value of the investment ( $115.76 ) is more than $115

Answer: False

B) As per the information provided in the question

The cost of air filter is =$25

Monthly Rate on interest is 1%

Annual rate of interest or capitalisation rate is = 1% x 12 =12% or 0.12

Annual capitalised cost = Cost of air filter / capitalisation rate

Annual capitalised cost = $25 / 0.12 = $208.33

Though the annual capitalised cost ( $208.33 ) is more than $200

Answer: True