Learning Outcomes. After watching this video, you will be able to, calculate the present and future values of an annuity due. Annuity due. In this video, we show how to calculate the present and future values of annuity dues. Remember, that an annuity due is one where the cash flows occur at the start of each time period. How do we calculate the present and future values of an annuity due? When compared to an ordinary annuity, each payment occurs one period earlier in an annuity due. So, we will have to bring forward each cash flow an additional period when computing future value. Denoting the future value of an n payment annuity due as FV Ad sub n. We can write FV Ad sub n is equal to FV A sub n times 1 + r over m. Using the formula for our future value of an ordinary annuity, FV A sub n, we get FV Ad sub n is equal to PMT times 1 + r over m, times within square brackets, 1 + r/m raised to the power of n- 1, the whole thing divided by r/m. Similarly, we can show that the present value today of an annuity due denoted as PV Ad sub 0 is PMT + PMT divided by r/m, times within square brackets, 1 over 1 plus r over n, the whole thing raised to the power of n minus 1. Let's look at an example. Previously we calculated the future value of a four-year $1000 a year ordinary annuity to be $4,641. The future value of a four-year $1000 a year annuity due would simply be $4641 times 1 plus 0.01, which equal $5105.10. You can verify that the formula for the future value of an annuity due, gives you the same answer. Let's look at another example, you have your eyes set on a new Audi A3, which sells for $34,000. You decide to borrow the entire amount from a bank which charges interest at 12% a year. The loan is for five years and the repayments to the bank will be on a monthly basis. The terms of the loan require you to start making the payments at the start of each period. How much will you pay the bank each month? Here you're given that the loan is an annuity due, so PV Ad sub 0 is 34,000. n is equal to 5 years x 12 months a year, which is 60 months, r is 12%, and m is equal to 12. You need to calculate the payment, PMT. Let's plugin all the values in the formula, PV Ad sub 0 is equal to PMT plus PMT divided by r over m, times within square brackets, 1 minus 1 over 1 plus r over m, the whole raised to the power of n minus 1. So, this gives us 34,000 is equal to PMT plus PMT divided by 0.12 over 12, times within square brackets, 1 minus 1 over 1 plus 0.12 over 12, the whole raised to the power of 59. Note, even though there are 60 payments in their annuity due, the denominator, within the square brackets, is raised to the power of 59. This is because, one payment occurs today, and the remaining payments form a 59 payment ordinary annuity. In other words, the present value of a 60 payment annuity deal is the sum of the first payment made today and the present value of the 59 payments ordinary annuity. So, now solving for PMT, we get the payment equals to $748.82. You will make 60 monthly payments of $748.82 every month with the first payment today. In the next video, we will look at what perpetuities are, and how they relate to stock valuation.