So let's look at an example where a farmer borrows $1,000

now and the interest rate is 7% per year.

And this is an unusual loan.

It's going to be repaid in total as a lump sum after five years.

So how big will that repayment need to be?

We plug those numbers into the formula.

$1000 is the present value, 7% is r, and 5 is t, the time.

And we can do the calculation and it turns out to be $1,402.

So we borrow money now, $1,000, and the cost

after five years is a bit over a $1,400.

So again, it shows that time really

matters once you have recognized the fact that upfront

costs have an interest cost.

So which time frame to use?

I've used five years and I've 20 years earlier on in the tree

planting example.

Which is the right time frame?

Well, there's no single right or wrong answer to this question.

It depends on the particular project, on the circumstances,

and on the preferences of who's making the decision.

So for farmers, for example, a realistic time frame

might be five years if they're on the verge of retiring

and they're not interested in benefits and costs

after that time.

Or 10 years or 20 years.

But for governments, they probably

have a longer time frame, maybe 20, 50.

Even as long as 100 years might be a realistic time frame

for governments to worry about.

Similarly, there's a question about which

interest rate to use.

I've used 5% and 7% in the example I've give so far,

but again, the right rate to use depends on the circumstances

and on who's making the decision.

For a farmer, borrowing funds might be more expensive,

risks might be more important, and risk

can be built into interest rates,

so the interest rate might be say, between 7% and 12%.

For government, funds are probably cheaper,

and their investments are highly diversified.

They've got so many different types of investment

that risk is less of a concern.

So the appropriate interest rate might be 5%, 6%, 7%,

in nominal terms.

So I'm going to explain what I mean

by nominal terms in a moment, but before I get to that,

I'm just going to comment that I'm talking here

about interest rates.

But we need to use this sort of thinking

of inflating upfront costs even if we're not paying interest,

because the funds that we are using

could have been invested in a bank account

and generated interest.

So we may not actually receive or pay interest,

but we could have done, and so we need to factor that in.

Nominal terms-- economists talk about nominal and real interest

rates, and nominal and real costs and benefits.

So we often adjust costs and benefits to allow for inflation

before we do other calculations, such as calculating

the present value or the future value.

So if we factor out inflation, that

means we're expressing our benefits and costs

in real terms.

If the inflation's left in, then we're

expressing the benefits and costs in nominal terms.

And we need to make sure that we use the right interest

rate for the right types of costs and benefits.

If we leave inflation in, then we're

using nominal benefits and costs and we

need to use a nominal interest rate, which leaves inflation

in.

If we factor inflation out of our benefits and costs,

we need to factor inflation out of our interest rate,

as well, which means using a real interest rate.

So the interest rate has to match the benefits and costs.

So here's this diagram we've seen before for the tree

example, where we have these upfront costs and benefits that

mainly occur later on.

And here's a table that shows exactly the numbers that

were in that diagram.

So the table also shows the calculation

of interest in the fifth column, and the future value

of the tree planting, which is at the bottom

of the sixth column.

But before we get to that, I'll just

point out that the first four columns are the same numbers as

appeared in earlier graphs.

So those first four columns are the year, the benefits,

the costs, and the net benefits.

And we've already seen those in one of the other of the graphs

that we've used previously for this example.

The last column shows the balance of this imaginary bank

account.

And the bottom of the last column

shows the balance at the end of the time period of 20 years.

So that's the criteria we're going to use.

If that's positive, it's good.

If that's negative, it's not good.

And in the fifth column, we can see the interest that's

paid or received on that balance in each of the years,

and that gets included in the balance.

So the benefits, the costs, and the interest

costs all go into determining the balance for that year.