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### Course: Macroeconomics>Unit 4

Lesson 8: Interest rates and the time value of money

# Present value 2

More choices as to when you get your money. Created by Sal Khan.

## Want to join the conversation?

• Say I would like to see what the risk free rate is today. How can I find that out? is there a website or anything that can tell you the risk free rate today?
• We assume that US government bonds are risk free. So any day you want, Just google 30 day treasury rate or 30 year treasury rate. The risk free rate goes up the longer you have to lock up your money so pick your amount of time and google away!
• Why did you use a 5% interest rate? Is it some benchmark rate or was it just random?
• It was not random, but was arbitrary, just like the \$100 was arbitrary. Sal chose a simple, round number to make it easy to see where everything goes when you do this kind of math.
• on the third choice, how come you did not consider the interest that the person could have earned with the 20 and 50 that were given to him. The person could have earned 5% on those two payments.
• The math works out to about the same. \$20 at 5% for a year yields \$21. Add the \$50, and \$71 at %5 yields \$74.05. Add the \$35, and you get \$109.05, less than either of the other two options. (P.S. Thank you, Sal, for teaching me how to do that in my head while I watch your vids!)
• Why compute backwards to present value instead of computing forwards to get the final amount? Either way you want the one with the bigger result in the end it seems.
• They both work when trying to determine which is worth more, but someone might just want to know what something is worth today. Really it's no more difficult, you just divide instead of multiply.
• Lets say i just add up \$20 + \$50 + \$35 = \$105 on the third one, then I just take the PV(105), is that possible?
• Not quite- you'd need to take the interest you'll receive from the \$20 and \$50 into account.
• I'm missing a nuance here and maybe someone can help. For the last option it seems to me you are really comparing what you could earn on the money if you invested each yearly payment till year 2 vs. if you got it all year one and invested it for two years vs. getting a larger amount in year 2. To my mind the correct way to calculate the third option is to: 20*1.05=21, then (21+50)*1.05=74.55, then for year 2 (74.55+35)*1.05= \$115.02. This is what you'd get if you invested the money yearly and it compounded, which is what you'd do in the real world. Can someone clarify?
• Close, Robert. \$20*1.05+\$50 (\$71) will be what you'll have at year 1. Then \$71*1.05+\$35 (\$109.55) will be what you'll have at year 2. You don't add the interest to the final amount (\$35) because you're just getting that now.
• Why do we use PV to select the best deal as opposed to comparing the future value? For example if we had a choice 4 with the highest future value (FV) after two years among the choices, would we choose choice 1 with the highest PV or choice 4 with the highest FV?
• We normally choose the option with the highest present value. This is because we have no idea when in the future we are going to need the money. As a result, we just use present value to approximate that.