An annuity is a series of payments that occur over time at the same intervals and in the same amounts. An annuity due arises when each payment is due at the beginning of a period; it is an ordinary annuity when the payment is due at the end of a period. A common example of an annuity due is a rent payment that is scheduled to be paid at the beginning of a rental period. Show
An example of an annuity is a series of payments from the buyer of an asset to the seller, where the buyer promises to make a series of regular payments. Thus, ABC Clothiers buys a warehouse from Dover Real Estate for $800,000, and promises to pay for the warehouse with eight payments of $100,000, to be paid at intervals of one payment per year; these payments are an annuity. You might want to calculate the present value of an annuity, to see how much it is worth today. This is done by using an interest rate to discount the amount of the annuity. The interest rate can be based on the current amount you are obtaining through other investments, the corporate cost of capital, or some other measure. An annuity table represents a method for determining the present value of an annuity. The annuity table contains a factor specific to the number of payments over which you expect to receive a series of equal payments and at a certain discount rate. When you multiply this factor by one of the payments, you arrive at the present value of the stream of payments. Thus, if you expect to receive 5 payments of $10,000 each and use a discount rate of 8%, then the factor would be 4.3121 (as noted in the table below in the intersection of the "8%" column and the "n" row of "5". You would then multiply the 4.3121 factor by $10,000 to arrive at a present value of the annuity of $43,121. Rate Table For the Present Value of an Annuity Due of 1The preceding annuity table is useful as a quick reference, but only provides values for discrete time periods and interest rates that may not exactly correspond to a real-world scenario. Accordingly, use the annuity formula in an electronic spreadsheet to more precisely calculate the correct amount of the present value of an annuity due. A series of equal payments made at the same interval at the start of each period What is Annuity Due?Annuity due refers to a series of equal payments made at the same interval at the beginning of each period. Periods can be monthly, quarterly, semi-annually, annually, or any other defined period. Examples of annuity due payments include rentals, leases, and insurance payments, which are made to cover services provided in the period following the payment. The annuity due can be illustrated as follows:  The first payment is received at the start of the first period, and thereafter, at the beginning of each subsequent period. The payment for the last period, i.e., period n, is received at the beginning of period n to complete the total payments due. Summary
Present Value of an Annuity DueThe present value of an annuity due uses the basic present value concept for annuities, except we should discount cash flow to time zero. The formula for the present value of an annuity due is as follows: Alternatively, Where:
The second formula is intuitive, as the first payment (PMT on the right side of the equation) is made at the start of the first period, i.e., at time zero; hence it comes without a discounting effect. Example An individual makes rental payments of $1,200 per month and wants to know the present value of their annual rentals over a 12-month period. The payments are made at the start of each month. The current interest rate is 8% per annum. Using the formula above: FV of the Investment = $1,200 x 11.57 FV of the Investment = $13,886.90 Future Value of an Annuity DueThe future value of an annuity due uses the same basic future value concept for annuities with a slight tweak, as in the present value formula above. To calculate the future value of an ordinary annuity: Where:
Example A company wants to invest $3,500 every six months for four years to purchase a delivery truck. The investment will be compounded at an annual interest rate of 12% per annum. The initial investment will be made now, and thereafter, at the beginning of every six months. What is the future value of the cash flow payments? Using the formula above: FV of the Investment = $3,500 x 10.49 FV of the Investment = $36,719.61 The calculations for PV and FV can also be done via Excel functions or by using a scientific calculator. Annuity Due vs. Ordinary Annuity1. PaymentsThe major difference between annuity due and the more popular ordinary annuity is that payments for an ordinary annuity are made at the end of the period, as opposed to annuity due payments made at the start of each period/interval. Ordinary annuity payments include loan repayments, mortgage payments, bond interest payments, and dividend payments. 2. Present valueAnother difference is that the present value of an annuity due is higher than one for an ordinary annuity. It is a result of the time value of money principle, as annuity due payments are received earlier. Hence, if you are set to make ordinary annuity payments, you will benefit from getting an ordinary annuity by holding onto your money longer (for the interval). Conversely, if you are set to receive annuity due payments, you will benefit, as you will be able to receive your money (value) sooner. In any annuity due, each payment is discounted one less period in contrast to a similar ordinary annuity. The relationship in equation terms can be illustrated as below: PV of an Annuity Due = PV of Ordinary Annuity * (1+i) Multiplying the PV of an ordinary annuity with (1+i) shifts the cash flows one period back towards time zero. The last difference is on future value. An annuity due’s future value is also higher than that of an ordinary annuity by a factor of one plus the periodic interest rate. Each cash flow is compounded for one additional period compared to an ordinary annuity. The formula can be expressed as follows: FV of an Annuity Due = FV of Ordinary Annuity * (1+i) Additional ResourcesThank you for reading CFI’s guide to Annuity Due. To keep learning and developing your knowledge base, please explore the additional relevant resources below:
What is a series of equal payments to be received at the beginning of each period for a finite period of time?An annuity is a series of equal cash flows, or payments, made at regular intervals (e.g., monthly or annually).
What is a series of equal payments to be received at the beginning of each period for a finite period time called quizlet?What is a series of equal payments for a finite period of time called? One characteristic of an annuity is that an equal sum of money is deposited or withdrawn each period. Holding all other variables constant, payment per period for an annuity due will be higher than an ordinary annuity.
What is a series of equal payments?A sequence of equal payments made at equal periods of time is called an annuity.
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What is a series of equal payments to be received at the beginning of each period?
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