Time value of money problems based on compouding frequency

CFA level I / Quantitative Methods: Basic Concepts / The Time Value of Money / Time value of money problems based on compouding frequency

The future value formula with known effective annual rate is:

FV = PV(1+EAR)^N

Putting the value of EAR in the above equation, we get:

FV = PV(1+r_s/m)^mN for all discrete frequencies

FV = PV*exp(r_s*N) for continuous compounding frequency

Example 8: Future value with different frequencies of compounding

Compute the future value of $100 after three years with annually, semi-annually, quarterly, monthly, continuously compounding frequency. The stated annual interest rate is 12 percent.

Solution:

Using the financial calculator:

Compounding frequency	PV	I/Y	N	FV
Annually	100	12/1 = 12	3*1=3	140.49
Semi-annually	100	12/2=6	3*2=6	141.85
Quarterly	100	12/4=3	3*4=12	142.58
Monthly	100	12/12=1	3*12=36	143.08
Continuously	100			143.33

For continuously compounding frequency, FV = PV*exp(r_s*N) = 100*exp(0.12*3) = $143.33.

To solve exp(0.36) on the financial calculator, you need to enter 0.36 and then press [2nd][e^x] buttons.

The future value amount grows with the increase in frequency because the compounding is done sooner and we earn more interest due to that.

Previous LOS: Effective annual rate based on stated annual rate and the frequency of compounding

Next LOS: Use of timeline in solving time value of money problems