Question

The nominal monthly rate for a loan is quoted at 5%. What is the equivalent annual rate? Semiannual rate? Continuous rate?

Answer 1

equivalent annual rate = 5.12%

Semiannual rate = 5.056%

Continuous rate is 4.99 %

Step-by-step explanation:

given data

nominal monthly rate = 5 %

solution

we get here equivalent annual rate that is

equivalent annual rate =
`(1+(0.05)/(12))^(12) - 1`

equivalent annual rate = 5.12%

and

now we get here Semiannual rate that is

`1+(r)/(2) = (1+(0.05)/(12))^(12)`

so Semiannual rate = 5.056%

and now we get here Continuous rate that is

`e^(r) = (1+(0.05)/(12))^(12)` = ln 12 ×
`(1+(0.05)/(12))` = 4.99 %

so Continuous rate is 4.99 %