# Conversion of 1- month effective interest rate to 6-month effective interest rate [closed]

I am given that the monthly effective interest rate is $1\%$ and I would like to find the $6$ month effective interest rate for a problem.

I used the formula $r_e=(1+r)^\frac{m}{n}-1=(1+.01)^\frac{12}{2}-1=.0615=6.15\%$

Since I am going from effective to effective interest, I am unsure if I should still use the effective interest formula. Or if this form of the formula is correct.

Any help is appreciated, I am having a hard time figuring out all the subtleties with interest rate.

## closed as off-topic by LocalVolatility, Helin, Bob Jansen♦Jan 29 '18 at 9:00

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – LocalVolatility, Helin, Bob Jansen
If this question can be reworded to fit the rules in the help center, please edit the question.

• I am voting to close this question for being too basic as per quant.stackexchange.com/help/on-topic. This topic is covered in the early chapters of most introductory textbooks such as Hull's "Options, Futures and Other Derivatives" or Sundaresan's "Fixed Income Markets and Their Derivatives". – LocalVolatility Jan 28 '18 at 1:38

## 1 Answer

I know that feeling when you get confused about different types of interest rates. I will try to help you out without using any formulas.

As far as I know an interest rate is called effectice if the corresponding time unit and the conversion period (i.e. the time where you get the interest) coincide.

If we consider your example of an effectife interest rate of $1\%$ for one month, this would mean that $100\$$would grow to 100* (1+0.01) = 101\$$ after one month For six months you would have six compounding periods, such that$100\$$would grow to 100 *(1+0.01)^6 = 106.152\$$.

This means that the six month effective interest rate is indeed $6.152\%$: $106.152\$ = 100 * (1+0.06152)^1\.