Question

4. How much is $100 worth 2 years from now if the annual rate of interest is 12% and compounding frequency is: (Hint: figure out the correct “m” and apply the FVn formula)

   1. a) Yearly

   2. b) 18 seconds

   3. c) 4.3 Months

   4. d) Every 4 years

Answer 1

- Invested amount today = $100

a). Calculating the Future Value after 2 years:-

Where,

r = Interest rate =12%

n= no of periods = 2 years

m = no of times compounding in a year = 1 (yearly compounding)

Future Value 2 years from now is $125.44

b). Calculating the Future Value after 2 years:-

Where,

r = Interest rate =12%

n= no of periods = 2 years

m = no of times compounding in a year = 31,536,000 seconds in a year/18 seconds = 1752,000 (As compounding every 18 seconds)

Future Value 2 years from now is $127.12

c). Calculating the Future Value after 2 years:-

Where,

r = Interest rate =12%

n= no of periods = 2 years

m = no of times compounding in a year = 12 months/4.3 months = 2.79069767441 (As compounding every 4.3 months)

Future Value 2 years from now is $126.49

d). Calculating the Future Value after 2 years:-

Where,

r = Interest rate =12%

n= no of periods = 2 years

m = no of times compounding in a year = 1 year/4 year = 0.25

Future Value 2 years from now is $121.66

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