Clearly the key here is going to be the interest rate that

converts these values over time.

So we can use our trusted equation of future value,

which equals present value into (1+r) raised to the power t.

And we have all the information in this problem to plug it in.

Future value of 15 million if we wait for five years, or

take the money now, 12 million.

And everything is going to depend on that interest rate,

because we know the time period.

So if you plug this into the financial calculator and get the value for r,

it actually works out to 4.56%.

In other words, if you think you can add more than 4.56% over the next five years,

take the 12 million now,

because its future value is going to be higher that 15 million.

If you think you'll earn less than 4.56%, wait until five years.

So this shows us by understanding and

determining interest rates, it's really key to good financial decision making.

Which is why we're going to spend a whole lecture on exploring just

how interest rates are set, why they are continuously changing, and

what impact they can have on the many decisions that we make.

So let's summarize what we've learned.

Time value is a process that explains how money is valued over time.

And to compute these values over time,

you can work with the basic future value equation and the present value formula.

So all the formulas we need are right here.

Future value is present value into (1+r) raised to the power t.

And then we're going to see a lot of applications where we have to compute

the present value, so

we just cross-multiply future value divided by (1+r) raised to the power t.

[COUGH] Now each of the formulas can be adjusted for

the frequency of compounding, as we mentioned, with this variable m.

So [COUGH] we can actually adjust these by dividing the interest rates by m,

so r would be divided by m and t would be multiplied by m, right?

[COUGH] This adjustment, of course, helps us to understand the relationship

between annual percentage rates and effective annual rates.

And here's our third formula to remember.

Effective annual rate is equal to 1 plus

the nominal annual percentage rate divided by m,

raised to the power m minus 1.