You have won the lottery! You are given two options for your p...

Question

You have won the lottery! You are given two options for your payout:

1. You can receive $540,000 today

2. You can receive $50,000 annually each year for the next twenty years

Assuming the interest rate is 6%, which is the better option?

Accepted Answer

Alright. Let's see how you guys did. You have won the lottery. You are given 2 options for your payout. And this is typically how lottery payouts go. So this is this is a very useful, time value of money application for when you guys win the lottery. Alright? So you either receive $540,000 today or you can receive $50,000 annually each year for the next 20 years. And that's usually how they do it. They'll say, lottery $1,000,000 But really what it means is that they're not going to just give you a $1,000,000 They're going to give you $50,000 for 20 years. And that's what a $1,000,000 payout is for a lottery. Okay? Still sounds pretty good. Hey, I would take it. But when you know time value of money, you know that that's not exactly worth a $1,000,000 Alright? So let's go ahead and see what's the better option. Should you take the $540,000 today? Or the $50,000 annually for the next 20 years? So we've got an interest rate, in this case, of 6%. So what do you see about option 1? We already know the present value of option 1, right? They told us. It's $540,000 today. So what is the present value of $540,000 today? It's $540,000, right? If I handed you $540,000 right now, you'd say, this is worth $540,000 Because it's in your hands right now, it's already the present. So the big deal here is to see if option 2 is worth more or less than the option option 1, the lump sum payment of $540,000. So let's go ahead and deal with option 2 here. So we're gonna have a timeline and, yes, it's gonna be a really long timeline because it's 20 years. What I'm gonna do is like a here, and then we'll get to the end. So we've got 0123 because nothing changes on all those years, 1920. Okay? So what's gonna happen is you're gonna get 50,000 per year. 50 k, I'm gonna put 50 k for 1,000 and that's gonna be every year. So year 4, 5, 6, all of those other years, you're gonna be getting $50,000 and we want to know what that stream of payments is worth today. What does it look like to you? Looks like an annuity, right? You're getting the same amount of money in equal periods, equal time passing in between each payment. So we have an annuity of $50,000 for 20 years. So we're going to use our table. Let's find the present value of this annuity using our table. So remember, what is the annuity payment? It's 50,000 in this case and we're going to multiply that by our present value factor which comes out of the table, right? So before we go to the table, we need to know 2 things. We need to know our n, number of periods. And we need to know our r, interest rate. In this case, n is going to be 20, right? We're dealing with 20 equal payments over 20 years. And what's our r in this case? R is the 6%, right? The 6% assumed interest rate that they told us in the problem. Alright? So knowing those two things, we're ready to go to our table. So let's go ahead and go to that sheet and which table are we going to use? Are we going to use the present value of $1 or the present value of ordinary annuity of $1? We're going to use the ordinary annuity, right? We just talked about how this is an annuity, so we use our annuity table to find the value. So in this case, we've got a, we said that our n is going to be 20, right? We've got 20 periods and it's 6%, right? Our interest rate was 6%, So we need to find that on the table, and that's going to be right here. 11.470. That is our present value factor for an annuity at 20 years at a rate of 6%. Percent. So let's go ahead and move back to our problem and we will see, the finale here. So 50,000 times, oh man, I forgot my number. I think it was 11.47, but my short term memory is getting away from me, got to go back down there. 11.470. Okay, that is our problem here. 11 0.470. Okay. So 11.470, let's go ahead and do that math. 50,000 times 11.47, it comes out to $573,500. Okay. So notice what we've got here. We've got option 1, $540,000 today or option 2 is a present value of these annuity payments of 5 $73,500. So in essence, option 2 is the better option, right? You're going to get more present value out of taking these annuity payments over the 20 years. And this is usually what happens when you have the lottery and they make these payments to you, it's generally going to be some sort of equation where by paying you over the next 20 years, you're going to end up getting more money than just taking a lump sum now. But what do people love? Money now. So they generally take that cut so that they can have that money right now. But now you know what's actually worth more, right? Taking those payments over the 20 year period. So you can always use your your present value tables once you win the lottery, and you can go ahead and figure out what's your best payment schedule once, once you find what they're going to pay you. Alright? So congrats here. Let's go ahead and move on to the next page.

Struggling with Financial Accounting?

You have won the lottery! You are given two options for your payout:
1. You can receive $540,000 today
2. You can receive $50,000 annually each year for the next twenty years
Assuming the interest rate is 6%, which is the better option?

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Struggling with Financial Accounting?

You have won the lottery! You are given two options for your payout:1. You can receive $540,000 today2. You can receive $50,000 annually each year for the next twenty yearsAssuming the interest rate is 6%, which is the better option?

Watch next

Using Time Value of Money Tables practice set

You have won the lottery! You are given two options for your payout:
1. You can receive $540,000 today
2. You can receive $50,000 annually each year for the next twenty years
Assuming the interest rate is 6%, which is the better option?