# Simple Formula for Converting Compound Interest Rates

This workbook has a simple formula to convert compound interest rates.

**=IF(t>500,f*LN(1+g/f),IF(f>=500,t*(EXP(g/t)-1),(t*((1+g/f)^(f/t))-t)))**

Where:

g = Current interest rate

f = Number of times the current rate compounds per year

t = Number of times the converted new rate compounds per year

This lookup table grabs two of the numbers for the formula

Continuous compounding in Excel is generally calculated as:

** =ln(1+r)**

The natural log of the annual rate

**=ln(1+5.0%)**

4.8790164169432%

Solving for the annual rate given the continuous rate

**=EXP(r)-1**

e raised to the power of the continuous rate

**=EXP(0.048790164169432)-1**

**5.00%**

e =2.71828182845904…

There is also a is a simpler version of the formula that can be copy/pasted into another worksheet without a lookup table:

Download workbook “Convert_Compound“

If the compond interest is 15% per year what is the simple interest

Spence,

It depends. Over what period of time? A $10,000 simple interest investment at 15% for two years, would earn $1,500 per year or $3,000. The same investment compounded annually, would earn $3,225. If you are asking for an equvilent interest rate, again it depends on the term. For the example above, the interest rate for a $10,000 investment worth $13,000 in two years would be equivalent to a 14.0175% compound annual interest rate. Do you have a specific type of loan or investment in mind? Can you give me an example?