1. Find Nominal interest rate, for Effective interest rate i = 10%, Compounded (n) = Monthly (12/year)
Solution:
`i=10%=0.1` per year (Effective interest rate)
`n=12` (Number of periods)
Nominal interest rate `i_(nom)=n xx((1+i)^(1/n)-1)`
`=12xx((1+0.1)^(1/12)-1)`
`=12xx((1.1)^(1/12)-1)`
`=12xx(1.008-1)`
`=12xx(0.008)`
`=0.0957`
`I_(nom)=i_(nom) xx 100=0.0957xx100=9.57 %`
2. Find Nominal interest rate, for Effective interest rate i = 20%, Compounded (n) = Yearly (1/year)
Solution:
`i=20%=0.2` per year (Effective interest rate)
`n=1` (Number of periods)
Nominal interest rate `i_(nom)=n xx((1+i)^(1/n)-1)`
`=1xx((1+0.2)^(1/1)-1)`
`=1xx((1.2)^(1/1)-1)`
`=1xx(1.2-1)`
`=1xx(0.2)`
`=0.2`
`I_(nom)=i_(nom) xx 100=0.2xx100=20 %`
3. Find Nominal interest rate, for Effective interest rate i = 10%, Compounded (n) = Continuously
Solution:
`i=10%=0.1` per year (Effective interest rate)
`n=0` (Number of periods)
Nominal interest rate `i_(nom)=ln(i+1)`
`=ln(0.1+1)`
`=ln(1.1)`
`=0.0953`
`I_(nom)=i_(nom) xx 100=0.0953xx100=9.53 %`
This material is intended as a summary. Use your textbook for detail explanation.
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