TLDR;
This video explains how to convert an effective interest rate to a nominal interest rate. It provides a step-by-step guide with examples for different compounding periods (monthly, quarterly, semi-annually, and daily). The key is to understand the formula and apply the correct order of operations, including taking roots and isolating the nominal interest rate variable.
- Converting effective interest rate to nominal interest rate.
- Step-by-step guide with examples.
- Different compounding periods (monthly, quarterly, semi-annually, and daily).
Introduction [0:00]
The video focuses on converting an effective interest rate to a nominal interest rate. The presenter emphasizes the importance of this skill in financial calculations.
Compounded Monthly [0:19]
The presenter begins with an example where interest is compounded monthly. The effective interest rate is given as 7% (0.07). The goal is to find the nominal interest rate. The formula involves raising (1 + nominal rate/12) to the power of 12, which equals (1 + effective rate). To solve for the nominal rate, the presenter advises taking the 12th root of (1 + 0.07), subtracting 1, and then multiplying by 12. The calculated nominal interest rate is 6.78%.
Compounded Quarterly [1:36]
Next, the presenter addresses a scenario with quarterly compounding. The effective interest rate remains at 7%. The setup involves using 4 as the compounding period. After performing similar calculations, the nominal interest rate is found to be 6.82%. The presenter shares a tip: the effective interest rate should always be slightly higher than the nominal interest rate.
Compounded Semi-Annually [2:03]
The video proceeds to demonstrate the conversion when interest is compounded semi-annually. The effective interest rate is still 7%. The equation is set up with a compounding period of 2. The presenter walks through the steps: taking the square root of (1 + 0.07), subtracting 1, and multiplying by 2. The resulting nominal interest rate is 6.88%.
Compounded Daily [3:05]
Lastly, the presenter tackles daily compounding. The effective interest rate is 7%. The compounding period is 365. The process involves taking the 365th root of (1 + 0.07), subtracting 1, and multiplying by 365. The nominal interest rate is calculated to be 6.77%.