Help with economics problems?

These problems are from a topic I learned called "Time Value of Money" (TVOM). The idea is that $1 today is worth more than $1 tomorrow because if the dollar were received today, we would be able to invest it or put it in the bank so it can gain interest and increase in value e.g. become $1.0001 the next day. There is also uncertainty to as to whether dollars can be achieved in the future. That is why the present value of money is always worth more than its future counterpart.

Are you guys given present value tables to use? Because my school gives them to us for problems like these. For reference, here is what we can refer to:

http://jcooney.ba.ttu.edu/fin3322/Brealey%20Files/...

1. This is just calculating the value of one amount. We can use the formula PV = FV/(1+r)^t

PV is Present Value, FV is Future Value, r is Rate, t is Time (also sometimes known as n for Number of periods).

FV = 1000, r = 10%, t = 10

PV = 1000/(1+0.10)^10

PV = 1000/(1.1)^10

PV = 1000/(2.59)

PV = 385.54 <--- That is how much your $1,000 in 10 years is worth today. This looks like a tiny figure but your interest rate is pretty high and it is over a long period. TVOM assumes interest is compound rather than fixed so take your answer (starting with 385.54) and multiply is by 1.1 ten times (NOT by 1.1x10). It is pretty amazing to see how much the money grows.

We can also just multiply our future value amount by the Table 1 factor at r = 10, t = 10.

$1000 x 0.386 = $386, and if we look at our above answer it is basically the same. The table is for convenience but the formula is more exact.

2. For this problem we will have to calculate the annuity. The formula for the present value of an annuity is modeled by: PVan = Annuity x (Table 3 factor)

To calculate the PV of the annuity, we can use the formula I used in the earlier question, which gives us $100,000/(1.01)^15 = $86,134.95.

$86,134.95 = Annuity x 13.87 <--- on Table 3 in the link, when t = 15 and r = 1, we get 13.87

$86,134.95/13.87 = Annuity

$6,210.16 = Annuity

With that said, you would have to pay $6,210.16 at the end of each year for 15 years at 1% to cover the mortgage of $100,000 which has a present value of $86,134.95.

The reason why we are using 13.87 instead of 15 because that value shown on the table accounts for the diminished value of the future dollar following the TVOM concept. A method of checking our answer is also referring to Table 1 (which shows the PV of $1 after t years).

Therefor we can take our annuity and multiply it by each number from 1-15 (each of the 15 years) in the 1% column of Table 1. So: 6210.16 x 0.99 + 6210.16 x 0.98 + 6210.16 x 0.971 ... + 6210.16 x 0.861 and you should get something similar to $86,134.95! My answer was $86,091.48 which is pretty close.

You might notice that if we add up all the values we will get 13.853, which is extremely similar to 13.87 from the other table. They are actually meant to be extremely similar if not the same, the one provided by my school was picture perfect, but some PV tables vary in accuracy and vagueness but they all deliver the same message, you get the jist of it!

This question was particularly confusing because I wasn't sure if the $100,000 had to be converted into present value terms or if it was already in those terms. In case you are curious, had we not converted it into PV terms we would have had an annuity of $7,209.81 and double checking would've given a value like $99,949, or something.

I hope I've cleared up some things and helped you understand this better.. I hope I didn't get them wrong... Anyways, good luck!

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It's possible for sure