Question

An investor can invest money with a particular bank and earn a stated interest rate of 15.40%; however, interest will be compounded quarterly. What are the nominal, periodic, and effective interest rates for this investment opportunity?

Answer 1

Nominal rate = 15.40%, Periodic rate = 3.85% and effective interest rate = 16.31%

Explanation:

An investor can invest money and earn a stated interest rate = 15.40%

We have to find the nominal, periodic and effective interest rates for this investment.

Nominal rate = Stated interest rate is also called annual percentage rate or nominal interest rate. Therefore nominal interest rate = 15.40%.

Periodic interest rate = Periodic interest rate is the annual interest rate divided by number of compounding periods.

Periodic rate = (
`(15.40)/(4)` ) = 3.85%

Effective interest rate = We have to calculate Effective interest rate (EAR) by the formula =
`EAR=[((1+i)/(n))^(n)-1]`

where i = rate of interest and n = number of compounding periods

`EAR=[(1+(0.154)/(4))^4]-1`

`EAR=[(1+.0385)^(4)]-1`

`EAR=[(1.0385)^(4)]-1`

EAR = 1.1631 - 1

EAR = 0.1631 = 16.31%

Therefore, Nominal rate = 15.40%, Periodic rate = 3.85% and effective interest rate = 16.31%