as the compounding rate becomes lower and lower, the future value of inflows approaches This is a topic that many people are looking for. s-star.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, s-star.org would like to introduce to you Future Value for Multiple Interest Rates . Following along are instructions in the video below:
“This video. I want to talk about how you calculate the future value with multiple multiple interest rates. Now usually. We re used to dealing with a problem where we one interest rate.
So we assume that you have this interest rate for 10 periods. And you want to find the future value in period 10. Then there s no problem we apply this formula. Here where the future value equals.
The present value times 1. Plus r raised to the t. Power. Where r is the interest rate.
And it s the same interest rate over the entire time period and t is the number of periods where compounding over but what happens if the interest rate changes someplace in the middle..
So i ve got an example here suppose you deposit 100 today and you d like to find the future value in year 8. But for the first 5 periods. You get an interest rate of 5 and then in periods. 6.
7. 8. You get an interest rate of 9. So this might be a little confusing.
But you re getting the interest rate between years 0 year 1 1. 2. All the way up to year 5 and then between 5 6. You re going to get the 9 between 6.
You ll get the 9 and between 7 8. You ll get the 9. So how you going to find the future value of this well. Perhaps the best way to think of this is to treat.
It as 2 steps so the future value in time period. 5. Is going to be we ll just use the formula. We have up.
Here a hundred. Times one. Plus the interest. Rate so 1 plus.
005 raised to the fifth..
Power and we re going to get 105. Why did the x key raises to a power fifth power times 100. And so we get 1 2763. So this is in your five its 127 63.
Now we can treat this as a lump sum in year 5. And we want to go out one to three more periods. But now these three periods will be compounded out at an interest rate of nine percent. So the future value in.
Year eight is going to be one twenty seven sixty three times 109. Raised to the third power. And so. Let s see what we get here one point zero.
Nine raise it to the third power and then times..
The one twenty seven lump sum 127. Sixty three we found in year five and we get 165 twenty eight so that s the way you go about dealing with the future value. When you have more than one interest rate. We could have had three interest rates for interest rates.
And if you were going to do this with more than one cash flow. You would have to use this procedure for all of the different cash flows. So you re going to find the future value or you re going to compound out by the appropriate interest rate for the number of periods that rate is in effect and then use the next interest rate for the next periods. The next number of periods that that rate is in effect.
But the easiest way to think of it is treat. It as two separate problems take this hundred dollars find the future value in year five. Now treat. This one 2763 is a lump sum and let s find the future value in year eight ” .
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