Calculating the Effective Interest Rate
1. Title Slide
What you can see on the screen here is the table constructed earlier in Excel, where we took a nominal interest rate of 10% and calculated the future value in 12 months time for different compounding frequencies. As you can see, as the compounding frequency increases, the future value also increases. So the effective rate must also be increasing. We can calculate the effective rate for each of the different compounding frequencies back in Excel. So scrolling down to this section called nominal rate versus effective rate, let's see if we can work out the effective rate when the nominal interest rate is 10%, but we change and increase the number of compounding periods within the year or F. So the present value, we want to start with 1000. The nominal rate was 10% and we're working this out one year from today. Now, we've done this table earlier in this chapter, but it never hurts to do a little bit of extra practice. So let's go on and quickly do that by referencing the present value and selecting F4 because now, when we just scroll down, we've got 1000 as our present value in each of the examples. The frequency, well annual compounding, the frequency is 1, semi annual compounding is 2, quarterly compounding is 4, monthly is 12, weekly is 52, and let's assume 365 days in the year. Now, what was our future values that we did earlier in this chapter? Well, we're gonna start with our present value, and we are gonna multiply that by open bracket 1 plus the nominal interest rate of 10%, which I'll absolutely reference and divide that by the compounding frequency close bracket. And we are gonna raise that all to the power of the number of years which is and again I'll absolutely reference that multiplied by the compounding frequency, which is in cell 1F134 close bracket. So the future value is 1110 when you've got annual compounding. And I can just fill that down now. And 'cause we've got the relative and absolute references in the right place, we see what our future values are for different compounding frequency. So effectively, what rate are you earning? Well, to work that out, we can take our ending value divided by our starting value and subtract the 1. And so you can see that the effective rate for annual compounding is 10%. It's the same as the nominal rate. And if I just highlight the column and Ctrl+D to fall down, you see that as the compounding frequency increases, the effective rate is also increasing.2. Let's practice!
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