# Present Value With Two Interest Rates

I want to provide an example of how you find the present value. If the interest rate changes during the time period, you're discounting by now normally when we find the present value of something we have one interest rate and the present value is defined to be equal to the future value in time, period and divided by 1, plus R raised to the nth power. Now suppose, for example, and I've got a little cash flow diagram here, we're receiving a thousand dollars five years from now.

And we want to find the. Present value today, but let's say that the interest rate, for example, is 8%. So R equals 8 percent in years 1 2, 3 and say, it goes up to 10% in years, 4 & 5. So how do we find the present value of that?

Well, we don't want to use 8% for all 5 periods because then we're ignoring the 10%. We also don't want to use 10% for all 5 periods because then we're using too high in interest rate for three of those periods. So this is the way we do it we're going to take the present value equals the thousand. And for. The first three, let me do the first two periods here are the last two periods. So the last two periods will be discounted by 1.10 raised to the second power.

So that will bring this back one two periods at the proprietary straight. And then we have to multiply by one point zero eight for the remaining three periods. So these last three periods will be discounted back at the 8% interest rate. So if we wanted to work that out, we could take one point, one and raise it to the second power. Okay, that's. One.

Point two one I'm going to save that so store one, and then 1.08 is going to be raised to the third power, whoops sorry, hit the Y to the X key raised up to the third power. And that equals one point, two, five, nine, seven one, two we're going to multiply that by the one point two one, which we stored in storage 1. So it's 1 point 5 2, 4. So that's, one point one o squared times. One point, oh, eight cubed. And we really want to flip that over okay.

So I'm going to hit the 1 over X key. And now I'll. Multiply it by. A thousand and we get six hundred and fifty-six dollars and six cents had, we used 10% for all five periods. We would have gotten too low a number. In fact, we can do that we can use our cash flow time value of money function keys here.

So we could have done it that way. N equals five interest rate is 10%. And the future value is a thousand, and we could have computed the present value, but we get to low it. We get to lower present value, because we use too high an interest rate for three of the periods. We.

Should have only used 8% here. We use 10%. Likewise, had we used 10% for all I'm sorry, had we used 8% for all three periods we'd have to higher present value. So we put that in everything else is the same compute. Present value. We get 680 58.

So we've ignored the 10%. So the correct way to do this is to use both interest rates for the appropriate number of periods. So we had 8% for three periods, and we had 10% for two periods.

Dated : 19-Apr-2022