Question

Compounding frequency, time value, and effective annual rates For each of the cases in the following table:

1. Calculate the future value at the end of the specified deposit period.
2. Determine the effective annual rate, EAR.
3. Compare the nominal annual rate, r, to the effective annual rate, EAR. What relationship exists between compounding frequency and the nominal and effec- tive annual rates?

Answer 1

1. we can consider the table below

compounding frequency: $FV_n=PV\times(1+r)^n$

A. $FV_5=\$2500\times (1.03)^{10}=\$3360$

B. $FV_3=50000\times(1.02)^{18}=\$71412$

C. $FV_{10}=1000\times (1.05)^{10}=\$1629$

D. $FV_6=20000\times (1.04)^{24}=\$51266$

2) effective annual rate: $EAR=(1+r/m)^m -1$

A. $EAR=(1+0.06/2)^2-1=1.061-1=0.061=6.1\%$

B. $EAR=(1+0.12/6)^6=1.126-1=0.126=12.6\%$

C. $EAR=(1+0.05/1)^1-1=1.05-1=0.05=5\%$

D. $EAR=(1+0.16/4)^4-1=1.170-1=0.17=17\%$

3) The effective rates of interest rise with increasing compounding frequency.