Find the present values of these ordinary annuities...

Find the present values of these ordinary annuities. Discounting occurs once a year. Do not round intermediate calculations. Round your answers to the nearest cent. $1,000 per year for 10 years at 6%. $ 7360.10 $500 per year for 5 years at 3%. $ $2,289.85 $300 per year for 5 years at 0%. $ 1500.00 Rework previous parts assuming they are annuities due. Present value of $1,000 per year for 10 years at 6%: $ value of $500 per year for 5 years at 3%: $ Present value of $300 per year for 5 years at 0%: $ 1500.00 I AM MISSING THOSE TWO, THE OTHERS ONES ARE CORRECT

Transcript

00:01 This annuity problem, we're going to do them one at a time.

00:03 Starting with the first one, we want to find out the present value.

00:09 R is the quantity of each payment, which is $1 ,000.

00:14 I is the interest rate, which is 10%.

00:20 And n is the number of periods, which is 16 years.

00:26 So to find the present value of an ordinary annuity, your formula is present value equals r times the present value of ordinary annuity with respect to n and i.

00:45 This bracketed piece has a formula to it.

00:50 I'll write it over to the side.

00:59 It's quite complex.

01:01 It's 1 minus 1 over 1 plus i to the n over i.

01:10 And instead of solving that, we are actually going to use a chart that you can find in a textbook for accounting or online.

01:21 So we're going to use that instead of using this formula for the answer to our problem here.

01:29 So present value equals r, which is a thousand times.

01:36 So here we're going to look up a number by looking up the column that has the correct input.

01:44 Rate, so in this case it's 10%.

01:46 And then we go down to the row that is number 16.

01:51 And for this one, that number is 7 .82371.

02:02 So when you multiply those numbers together, you get 78, 23, and 71 cents.

02:08 That's the answer to the first part.

02:10 Now when you talk about an annuity due, that means the first payment is at the beginning of the period instead of the end of the period...

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