Question

A loan shop in town offers emergency loans of up to $800 for 1 month. The shop charges a 4% fee of the amount for the 1-month period. If a person borrows $800for one month, what is:

1. the nominal interest rate per year?
2. the effective rate per year?

Answer 1

If the fees are taken at the end of the month:

The fee is the interest rate per month on the amount borrowed. It is effective per month interest rate.

a)

nominal annual interest rate =effective per month rate * total months in a year=4*12=48 %

the nominal interest rate per year is 48%

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b)

The formula for an effective annual interest rate is:

The effective annual interest rate is 60.10%

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if the fees are taken at the time of borrowing:

then

An effective amount of borrowed =800-800*0.04=768

and returned amount after month is $800

so effective monthly interest amount =800-768=32

effective monthly interest rate =((32/768))*100=4.16666667

Nominal annual interest rate =4.16666667*12=50%

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Effective annual interest rate is:

In most of the cases, the fees are charged first, so the second part is most suitable for it.