1. Find Effective interest rate, for Nominal interest rate i = 10%, Compounded (n) = Monthly (12/year)
Solution:
`i=10%=0.1` per year (Nominal interest rate)
`n=12` (Number of periods)
Effective interest rate `i_(eff)=(1+i/n)^n-1`
`=(1+0.1/12)^12-1`
`=(1+0.0083)^12-1`
`=(1.0083)^12-1`
`=1.1047-1`
`=0.1047`
`I_(eff)=i_(eff) xx 100=0.1047xx100=10.47 %`
2. Find Effective interest rate, for Nominal interest rate i = 20%, Compounded (n) = Yearly (1/year)
Solution:
`i=20%=0.2` per year (Nominal interest rate)
`n=1` (Number of periods)
Effective interest rate `i_(eff)=(1+i/n)^n-1`
`=(1+0.2/1)^1-1`
`=(1+0.2)^1-1`
`=(1.2)^1-1`
`=1.2-1`
`=0.2`
`I_(eff)=i_(eff) xx 100=0.2xx100=20 %`
3. Find Effective interest rate, for Nominal interest rate i = 10%, Compounded (n) = Continuously
Solution:
`i=10%=0.1` per year (Nominal interest rate)
`n=0` (Number of periods)
Effective interest rate `i_(eff)=e^i-1`
`=2.7183^0.1-1`
`=1.1052-1`
`=0.1052`
`I_(eff)=i_(eff) xx 100=0.1052xx100=10.52 %`
This material is intended as a summary. Use your textbook for detail explanation.
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