You are saving up $12,000 for a luxurious European vacation tw...

Question

You are saving up $12,000 for a luxurious European vacation two years from now. How much money would you need to invest today at Clutch Bank, earning their juicy 10% annual interest, to have enough for your vacation?

Accepted Answer

Alright. Let's see how you did. You're saving up $$12,000 for a luxurious European vacation 2 years from now. How much money would you need to invest today at Clutch Bank, earning their juicy 10% interest rate to have enough for your vacation. So notice, you want to have 12$$,000 2 years from now, not $$12,000 right now. You're going to earn interest on whatever you put in today to get you up to 12$$,000 So this $$12,000 that's a future value right there, right? That's what we want to have in the future. And how long till we have that? 2 years from now. That is our N, right? Our N is going to be 2 years from now. And what else did it give us? It told us that our interest rate is 10%. That's our interest rate R. So knowing all of that, we can solve for the present value. How much do we invest today so that it can earn interest at 10% and be worth 12$$,000 So our present value well, let's do a timeline here too. Let's do a timeline real quick. So we've got 2 years, so we have right now and then 2 years in the future. So there's $$12,000 that we wanna have 2 years in the future, so we wanna know what is that worth today so that we can earn interest over the next 2 years and get that money. Cool? And this is again at 10% interest. So let's go ahead and do our equation. We're gonna have our present value which is what it's worth today equal to the future value. So what's the future value? 12,000, right? That's what we wanna have in 2 years divided by 1+R. So what was our R in this situation? 10% again. Right? 0.10 as a decimal and it's to the nth power, which in this case is 2. Right? 2 years from now. So there we go. Remember that this is future value divided by 1+r to the n. So, it gave us all those variables. All we need to do is solve for do basically use our calculator to solve this now. So we can simplify 12,000 divided by 1.10 squared. So let's do that 1.10 squared first so that we just have a number in the denominator. 1.1 times 1.1, it gives us 1.21. So 12,000 divided by 1.21, it comes out to, we'll say approximately 9$$,917 and a few cents here, right? $$9,917 that's what you would need to invest today so that in 2 years, you would have 12$$,000. You can even check that out. Go ahead and do $$9,917 add 10% interest to it, add another 10% interest to it, and of course, we'll be a little off because of rounding, but you'll have that 12$$,000 2 years from now. Cool? Let's pause here and let's try the second one down below.

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You are saving up \$12,000 for a luxurious European vacation two years from now. How much money would you need to invest today at Clutch Bank, earning their juicy 10% annual interest, to have enough for your vacation?

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