And the present value of all of this of course given to us which is $5,000.

So we'll just put that amount here, time zero, we know it's 5,000.

So, how do we find those particular payments?

Well, this looks like an ordinary annuity, we want the present value of that annuity.

So we're going to equate this present value with the formula for

the annuity and we know that all too well by now.

So we take the annuity which is what we're looking for, in this case it's x.

And we're going to multiply this by the annuity factor which is 1

minus 1 over 1 plus r raised to the power t the whole thing over r.

Remember this is the present value annuity factor for r % t periods.

Right, all we have to do now is plug the numbers in and

if we do that what do we get.

Well 5,000 equals to x.

We're still looking for that,

multiply that by the factor which is 1 minus 1 over 1 point.

In this example we have to be careful and use the correct monthly rate.

We know the annual rate.

The annual rate has been given to us, which is in fact 9%.

So, the annual rate is 9%.

We want to convert this to a monthly rate and

the frequency of compounding of course is 12, 12 months in a year.

So that we adjust r by m and that would be 9% divided by 12,

which gives us the monthly rate of 0.0075.

That's the rate we want to plug in here.

So 1- 1 / 1 + the rate 0.007, missed a zero there,

0.0075 raised to the power 36.

And the whole thing of course divided by R which is .0075, right?

We solve for this, we know this equals to $5,000 and

your payments are going to work out to be $158.99 or about 159.

Question number five.

Again, we can visualize the information on a timeline.

You're making equal biweekly deposits for 35 years in the future.

And this time, you're given a future value which is $1 million.

All right, but if this is bi-weekly lets start with something we

know which is that there are 52 weeks in the year.

And since you make deposits every two weeks you will

make 26 deposits in a year for a total of 26 deposits

times 35 years which is 910 deposits, right?

So let's put this on a timeline.

We've got from zero, right,

until 910 deposits, right?

And if you're wondering how I did the math quickly for

910, remember that we have 52 weeks in a year.

And we're biweekly deposits that means every two weeks.

So if we divide that by two we get 26 deposits,

and 26 deposits is occurring over 35 years.

And that gives the 910 periods.